# Recent questions tagged convergent

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Determine $5+12+19+\cdots+54$
Determine $5+12+19+\cdots+54$Determine $5+12+19+\cdots+54$ ...
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Determine the value of the series: $\sum_{k=4}^{7} 2 k$
Determine the value of the series: $\sum_{k=4}^{7} 2 k$Determine the value of the series: \ \sum_{k=4}^{7} 2 k \ ...
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Determine the value of the series: $\sum_{n=1}^{5}(3 n+2)$
Determine the value of the series: $\sum_{n=1}^{5}(3 n+2)$Determine the value of the series: \ \sum_{n=1}^{5}(3 n+2) \ ...
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Determine, giving reasons, whether the sequence $\left\{a_{n}\right\}=\left\{\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right\}$ is convergent or divergent. If it is convergent, find the value to which it converges.Determine, giving reasons, whether the sequence $\left\{a_{n}\right\}=\left\{\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right\}$ is convergent or diverge ...
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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. $\sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}$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. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$
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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Find the limit of the sequence $\left\{\dfrac{-1}{(-1)^{n}}\right\}$ (if it exists).
Find the limit of the sequence $\left\{\dfrac{-1}{(-1)^{n}}\right\}$ (if it exists).Find the limit of the sequence $\left\{\dfrac{-1}{(-1)^{n}}\right\}$ (if it exists). ...
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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. 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, giving reasons, whether the sequence $$\left\{a_{n}\right\}=\left\{\frac{5-n+3 n^{2}}{7 n^{2}-19}\right\}$$ is convergent or divergent. If it is convergent, state to what value it converges.Determine, giving reasons, whether the sequence $$\left\{a_{n}\right\}=\left\{\frac{5-n+3 n^{2}}{7 n^{2}-19}\right\}$$ is convergent or divergent. I ...
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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. $\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$Decide (with reasons) if the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$ ...
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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.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$ ...
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Determine if the following series converge $\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$
Determine if the following series converge $\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$Determine if the following series converge $\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$ ...
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Determine if the following series converge $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$
Determine if the following series converge $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$Determine if the following series converge $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$ ...
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For which values of $x$ will $\sum_{k=1}^{\infty}(4 x-1)^{k}$ exist.
For which values of $x$ will $\sum_{k=1}^{\infty}(4 x-1)^{k}$ exist.For which values of $x$ will \ \sum_{k=1}^{\infty}(4 x-1)^{k} \ exist. ...
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Calculate $S_{\infty}$ if $\sum_{p=1}^{\infty} 8(4)^{1-p}$
Calculate $S_{\infty}$ if $\sum_{p=1}^{\infty} 8(4)^{1-p}$Calculate $S_{\infty}$ if \ \sum_{p=1}^{\infty} 8(4)^{1-p} \ ...
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For $\alpha=(1+\sqrt{5}) / 2$ and $\beta=(1-\sqrt{5}) / 2$, show that $\sum_{\mathrm{k}=0}^{\infty} \beta^{k}=-\beta=\alpha-1$ and that $\sum_{k=0}^{\infty}|\beta|^{\mathrm{k}}=\alpha$For $\alpha=(1+\sqrt{5}) / 2$ and $\beta=(1-\sqrt{5}) / 2$, show that $\sum_{\mathrm{k}=0}^{\infty} \beta^{k}=-\beta=\alpha-1$ and that \(\sum_{ ...
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Determine the first term and the constant difference if $T_{n}=11-6 n$.
Determine the first term and the constant difference if $T_{n}=11-6 n$.Determine the first term and the constant difference if $T_{n}=11-6 n$. ...
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Which of the following statements about the series $$\sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}}$$ is true?
Which of the following statements about the series $$\sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}}$$ is true?Which of the following statements about the series $$\sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}}$$ is true? ...
A convergent geometric series consisting of only positive terms has first term $a$, constant ratio $r$ and $n^{\text {th }}$ term, $T_{n}$, such that $\sum_{n=3}^{\infty} \mathrm{T}_{n}=\frac{1}{4}$. A convergent geometric series consisting of only positive terms has first term $a$, constant ratio $r$ and $n^{\text {th }}$ term, $T_{n}$, such tha ...
By using a suitable Maclaurin series given in the text find the sum to infinity of the following infinite series:By using a suitable Maclaurin series given in the text find the sum to infinity of the following infinite series: (a) $\pi-\frac{\pi^{3}}{3 !}+\frac{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the value of$x$given the equation:$\dfrac{3}{5}(x+2)=12$1 answer 93 views What is the value of$x$given the equation:$\dfrac{3}{5}(x+2)=12$What is the value of$x$given the equation:$\dfrac{3}{5}(x+2)=12$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A geometric series has a constant ratio of$\frac{1}{2}$and a sum to infinity of 6. 1 answer 515 views A geometric series has a constant ratio of$\frac{1}{2}$and a sum to infinity of 6. A geometric series has a constant ratio of$\frac{1}{2}$and a sum to infinity of 6. Calculate the first term of the series. Calculate the ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If$5^{-x}=10$, determine the value of$\dfrac{2^{x-1}+2^{x+1}}{5 \times 10^{x}}$1 answer 113 views If$5^{-x}=10$, determine the value of$\dfrac{2^{x-1}+2^{x+1}}{5 \times 10^{x}}$If$5^{-x}=10$, determine the value of$\dfrac{2^{x-1}+2^{x+1}}{5 \times 10^{x}}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If$\frac{x}{3}=12$, determine the value of$\frac{x}{4}$. 1 answer 112 views If$\frac{x}{3}=12$, determine the value of$\frac{x}{4}$.If$\frac{x}{3}=12$, determine the value of$\frac{x}{4}$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Grade 12 - Paper 1 - If$\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of$p$. 1 answer 152 views Grade 12 - Paper 1 - If$\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of$p$.If$\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of$p$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Grade 12 Paper 1 - Prove that$\sum_{k=1}^{\infty} 4.3^{2-k}$is a convergent geometric series. Show ALL your calculations. 1 answer 241 views Grade 12 Paper 1 - Prove that$\sum_{k=1}^{\infty} 4.3^{2-k}$is a convergent geometric series. Show ALL your calculations.Prove that$\sum_{k=1}^{\infty} 4.3^{2-k}\$ is a convergent geometric series. Show ALL your calculations. ...