List questions from telescopic-series

Published on 11 May 2026 - 0:19

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Evaluate $\lim_{n \to \infty}\prod_{k=0}^{n} \left(1+\frac{2}{45^{2^k}+45^{-2^k}}\right)$

Published on 16 Apr 2026 - 18:54

94

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Show that this inequality is true

Published on 13 Apr 2026 - 23:48

441

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Sum of finite series using partial fraction

Published on 10 Apr 2026 - 20:37

55

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Le=t $0<a_1<b_1$ For $n\geq 1$, define $a_{n+1}=\sqrt{a_n b_n}$ and $b_{n-1}=\frac{a_n+b_n}{2}.$ Then

Published on 16 Apr 2026 - 15:18

544

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Prove sum of $k^2$ using $k^3$

Published on 09 Apr 2026 - 22:44

131

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sum upto n terms where rth term is $r(r+1)2^r$

Published on 12 Apr 2026 - 14:53

182

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Find the sum of the series with terms given by ${T}_{r}=\frac{r}{(r+1)(r+3)(r+4)}$

Published on 12 Apr 2026 - 19:26

86

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prove formula by induction

Published on 12 Apr 2026 - 19:23

161

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How to find the sum of this series? is there any simple way?

Published on 13 Apr 2026 - 16:34

162

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Find the sum: $\sum_{n=1}^{20}\frac{(n^2-1/2)}{(n^4+1/4)}$

Published on 16 Apr 2026 - 22:56

1.9k

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If $\sum_{r=0}^{n-1}\log _2\left(\frac{r+2}{r+1}\right)= \prod_{r = 10}^{99}\log _r(r+1)$, then find $n$.

Published on 14 Apr 2026 - 0:17

153

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How to find this telescoping Sum of $\sum_{n=1}^{50} \frac{n}{n + n^2 + n^4} \\$?

Published on 15 Apr 2026 - 4:05

2.3k

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The number of ways to represent a natural number as the sum of three different natural numbers

Published on 12 Apr 2026 - 2:27

79

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Is this series $\sum_{n=0}^\infty(\frac{n}{2n^2-1})^2$ convergent?

Published on 15 Apr 2026 - 8:41

List Question

Evaluating $\int_0^n \{x^2\}\,\text{d}x$

Evaluate $\lim_{n \to \infty}\prod_{k=0}^{n} \left(1+\frac{2}{45^{2^k}+45^{-2^k}}\right)$

Show that this inequality is true

Sum of finite series using partial fraction

Le=t $0<a_1<b_1$ For $n\geq 1$, define $a_{n+1}=\sqrt{a_n b_n}$ and $b_{n-1}=\frac{a_n+b_n}{2}.$ Then

Prove sum of $k^2$ using $k^3$

sum upto n terms where rth term is $r(r+1)2^r$

Find the sum of the series with terms given by ${T}_{r}=\frac{r}{(r+1)(r+3)(r+4)}$

prove formula by induction

How to find the sum of this series? is there any simple way?

Find the sum: $\sum_{n=1}^{20}\frac{(n^2-1/2)}{(n^4+1/4)}$

If $\sum_{r=0}^{n-1}\log _2\left(\frac{r+2}{r+1}\right)= \prod_{r = 10}^{99}\log _r(r+1)$, then find $n$.

How to find this telescoping Sum of $\sum_{n=1}^{50} \frac{n}{n + n^2 + n^4} \\$?

The number of ways to represent a natural number as the sum of three different natural numbers

Is this series $\sum_{n=0}^\infty(\frac{n}{2n^2-1})^2$ convergent?

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