List questions from telescopic-series

Published on 26 Feb 2026 - 3:22

95

Views

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

Published on 22 Apr 2020 - 14:38

91

Views

Show that this inequality is true

Published on 11 May 2020 - 20:26

438

Views

Sum of finite series using partial fraction

Published on 16 May 2020 - 21:07

52

Views

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 23 May 2020 - 4:42

541

Views

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

Published on 31 May 2020 - 9:36

128

Views

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

Published on 04 Jun 2020 - 13:58

179

Views

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

Published on 16 Jun 2020 - 15:56

83

Views

prove formula by induction

Published on 30 Jun 2020 - 21:14

158

Views

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

Published on 10 Jul 2020 - 10:36

159

Views

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

Published on 13 Jul 2020 - 12:48

1.9k

Views

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 19 Jul 2020 - 9:37

150

Views

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

Published on 24 Jul 2020 - 15:10

2.3k

Views

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

Published on 25 Jul 2020 - 4:27

76

Views

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

Published on 25 Jul 2020 - 7:54

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?

Trending Questions

Popular # Hahtags

Popular Questions