# Recent questions tagged infinite

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Let $\mathcal{S}$ be the linear space of infinite sequences of real numbers $x:=\left(x_{1}, x_{2}, \ldots\right) .$ Define the linear map $L: \mathcal{S} \rightarrow \mathcal{S}$ byLet $\mathcal{S}$ be the linear space of infinite sequences of real numbers $x:=\left(x_{1}, x_{2}, \ldots\right) .$ Define the linear map \(L: \m ...
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Which of the following statements is NOT TRUE?
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Which of the following statements is NOT TRUE?Which of the following statements is NOT TRUE? &nbsp; (A) $\int_{0}^{3} \frac{1}{(x-4)^{2}} d x=\frac{3}{4}$. (B) $\int_{0}^{3} \frac{1}{(x-4)^{2}} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Consider the series$\sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}$. Which of the following statements is TRUE? 0 answers 7 views Consider the series$\sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}$. Which of the following statements is TRUE?Consider the series$\sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}$. Which of the following statements is TRUE? &nbsp; (A) The series is not conditiona ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$g(x, y)=x^{2} y+\cos y+y \sin x$, Which of the following statements is TRUE? 0 answers 5 views Let$g(x, y)=x^{2} y+\cos y+y \sin x$, Which of the following statements is TRUE?Let$g(x, y)=x^{2} y+\cos y+y \sin x$Which of the following statements is TRUE? &nbsp; (A)$g_{x}=2 x y+\cos y+y \cos x$. (B)$g_{y}=2 x-\sin y+\s ...
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Consider the telescoping series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$.
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Consider the telescoping series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$.Consider the telescoping series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$. ...
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Show that the series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$ converges and find its sum.
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Show that the series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$ converges and find its sum.Show that the series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$ converges and find its sum. ...
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}$
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}$Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}$ ...
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$ ...
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Given that $\dfrac{1}{1-x}=1+x+x^{2}+x^{3}+\cdots=\sum_{n=0}^{\infty} x^{n}$. Write down the power series of $\dfrac{1}{1+x^{2}}$
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Given that $\dfrac{1}{1-x}=1+x+x^{2}+x^{3}+\cdots=\sum_{n=0}^{\infty} x^{n}$. Write down the power series of $\dfrac{1}{1+x^{2}}$Given that $\dfrac{1}{1-x}=1+x+x^{2}+x^{3}+\cdots=\sum_{n=0}^{\infty} x^{n}$. Write down the power series of $\dfrac{1}{1+x^{2}}$ ...
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The interval of convergence of the series $\sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n}$ is
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The interval of convergence of the series $\sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n}$ isThe interval of convergence of the series $\sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n}$ is &nbsp; A. $\quad(-3,-1$ &nbsp; B. $-3,-1$ &nbs ...
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Which FIVE of the following statements are TRUE?
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Which FIVE of the following statements are TRUE?Which FIVE of the following statements are TRUE? &nbsp; A. The series $\sum_{n=1}^{\infty}\left(\frac{4 n-3}{3 n-4}\right)^{n}$ converges &nbsp; B ...
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If the power series of $f$ at $a$ is given by $$f(x)=\sum_{n=0}^{\infty} c_{n}(x-a)^{n}$$ for $|x-a|<R$, then
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If the power series of $f$ at $a$ is given by $$f(x)=\sum_{n=0}^{\infty} c_{n}(x-a)^{n}$$ for $|x-a|<R$, thenIf the power series of $f$ at $a$ is given by $$f(x)=\sum_{n=0}^{\infty} c_{n}(x-a)^{n}$$ for $|x-a|&lt;R$, then ...
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Determine whether the series $\sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}}$ converges or diverges. Give a reason for your answer.
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Determine whether the series $\sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}}$ converges or diverges. Give a reason for your answer. Determine whether the series $\sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}}$ converges or diverges. Give a reason for your answer. ...
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Find the sum of the series $\sum_{n \geq 2} \frac{2}{n^{2}-1}$
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Find the sum of the series $\sum_{n \geq 2} \frac{2}{n^{2}-1}$Find the sum of the series $\sum_{n \geq 2} \frac{2}{n^{2}-1}$ ...
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$ ...
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Which of the following statements is incorrect?
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Which of the following statements is incorrect?Which of the following statements is incorrect? &nbsp; A. If $c \neq 0$ and $\left(a_{n}\right)$ converges, then $\left(c a_{n}\right)$ converges. ...
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The series $$\sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}$$
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The series $$\sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}$$The series $$\sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}$$ A. is a convergent geometric series with $\sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that if the series$\sum_{n=1}^{\infty} a_{n}$converges, then$\lim _{n \rightarrow \infty} a_{n}=0$. 0 answers 6 views Prove that if the series$\sum_{n=1}^{\infty} a_{n}$converges, then$\lim _{n \rightarrow \infty} a_{n}=0$.Prove that if the series$\sum_{n=1}^{\infty} a_{n}$converges, then$\lim _{n \rightarrow \infty} a_{n}=0$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$0 answers 7 views Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$0 answers 7 views Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The series$ \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}} $0 answers 6 views The series$ \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}} $The series $$\sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}$$ A. is a convergent geometric series with$\sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1} ...
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Using the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansion
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Using the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansionUsing the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansion A. $\quad 1+x^{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine if the following series converge$\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$0 answers 5 views Determine if the following series converge$\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$Determine if the following series converge$\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine if the following series converge$\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$0 answers 6 views Determine if the following series converge$\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$Determine if the following series converge$\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that the series$ \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)}$converges and find its limit. 0 answers 10 views Show that the series$ \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)}$converges and find its limit.Show that the series$ \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)}\$ converges and find its limit. ...
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