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Recent questions tagged convergent


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Determine \(5+12+19+\cdots+54\)
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Determine \(5+12+19+\cdots+54\)Determine \(5+12+19+\cdots+54\) ...
by MathsGee Platinum
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asked in Mathematics Apr 8
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Determine the value of the series: \[ \sum_{k=4}^{7} 2 k \]
1 answer 69 views
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Determine the value of the series: \[ \sum_{n=1}^{5}(3 n+2) \]
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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. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$

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Find the limit of the sequence $\left\{\dfrac{-1}{(-1)^{n}}\right\}$ (if it exists).
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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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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.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$
0 answers 40 views
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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 $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$
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For which values of \(x\) will \[ \sum_{k=1}^{\infty}(4 x-1)^{k} \] exist.
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Calculate \(S_{\infty}\) if \[ \sum_{p=1}^{\infty} 8(4)^{1-p} \]
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Determine the first term and the constant difference if $T_{n}=11-6 n$.
1 answer 94 views
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Which of the following statements about the series $$ \sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}} $$ is true?
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By using a suitable Maclaurin series given in the text find the sum to infinity of the following infinite series:
1 answer 258 views
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{ ...
by Student SIlver Status
(10,904 points)
asked in Mathematics May 23, 2021
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What is the value of $x$ given the equation: $\dfrac{3}{5}(x+2)=12$
1 answer 93 views
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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 ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics May 19, 2021
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If $5^{-x}=10$, determine the value of $\dfrac{2^{x-1}+2^{x+1}}{5 \times 10^{x}}$
1 answer 113 views
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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 $\frac{x}{4}$. ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics May 12, 2021
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Grade 12 - Paper 1 - If $\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of $p$.

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Grade 12 Paper 1 - Prove that $\sum_{k=1}^{\infty} 4.3^{2-k}$ is a convergent geometric series. Show ALL your calculations.
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