Question

A converse to a lemma of Cesàro?

score 77 · Answer 1 · 2021-03-29 00:58:22

77

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A converse to a lemma of Cesàro?

Published on 29 Mar 2021 - 0:58

score 218 · Answer 2 · 2021-03-29 23:06:58

218

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How do I evaluate $\sum_{n=1}^{\infty}\frac{n}{2n-1} - \frac{n+2}{2n+3}$?

Published on 29 Mar 2021 - 23:06

score 144 · Answer 3 · 2021-04-02 16:38:42

144

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How many real solutions does the equation $f(x) =0$ have, where $f(x) =\sum_{i=1}^{2020} \frac {i^2}{\left( x-i\right)} $

Published on 02 Apr 2021 - 16:38

score 96 · Answer 4 · 2021-04-05 15:25:42

96

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Alternative method to showing that $\sum_{r=-\infty}^{\infty}\frac{1}{64r^4+1}=\frac{\pi}{4}\frac{1+\sinh(\pi/2)}{\cosh(\pi/2)}$

Published on 05 Apr 2021 - 15:25

score 53 · Answer 5 · 2021-04-06 05:49:16

53

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If $S_{n,m}=\sum_{k=1}^{n} k^m =\sum_{j=0}^{m-1} A_{n,j}(m) S_{n,j},$ what are $A_{n,j}(m)$

Published on 06 Apr 2021 - 5:49

score 632 · Answer 6 · 2021-04-09 00:46:10

632

Views

$\sum_{n=1}^\infty\frac{n}{(2n-1)16^n}\binom{2n}{n}^2\left(\sum_{k=n}^\infty\frac{2^k}{k\binom{2k}{k}}\right)=1-\sqrt2+\log(1+\sqrt2).$

Published on 09 Apr 2021 - 0:46

score 209 · Answer 7 · 2021-04-10 22:35:55

209

Views

Prove that $\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{F_kF_{k+1}}=\frac{1}{\phi}$.

Published on 10 Apr 2021 - 22:35

score 163 · Answer 8 · 2021-04-14 12:13:49

163

Views

Partial sum estimate for $\sum_{p\leq x} \frac{1}{p^{1/2}}$

Published on 14 Apr 2021 - 12:13

score 104 · Answer 9 · 2021-05-03 14:41:45

104

Views

Does my odd proof for the Abel sum for $\eta(-2)$ work?

Published on 03 May 2021 - 14:41

score 322 · Answer 10 · 2021-05-12 07:02:25

322

Views

How to evaluate the following sum?

Published on 12 May 2021 - 7:02

score 94 · Answer 11 · 2021-05-22 18:15:17

94

Views

About the limit $\lim_{x\to 1^-} (1-x)\sum_{n\ge 0} a_n x^n=L$

Published on 22 May 2021 - 18:15

score 57 · Answer 12 · 2021-05-25 08:04:01

57

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Finding $\sum_{0 \le r <s \le n}~ (r+s){n \choose r}{n \choose s}$

Published on 25 May 2021 - 8:04

score 50 · Answer 13 · 2021-05-26 04:58:58

50

Views

What summation rule am I missing here?

Published on 26 May 2021 - 4:58

score 84 · Answer 14 · 2021-05-28 18:15:49

84

Views

Properties of $\sum _{l=0}^{\infty } \left( -1 \right) ^{l}{m+l-1\choose l} \left( 2 \,{\frac {l}{m}}+1 \right) ^{1-\nu}$

Published on 28 May 2021 - 18:15

score 186 · Answer 15 · 2021-05-31 21:28:28

186

Views

In search for a counterexample related to the Abel-Stolz theorem

Published on 31 May 2021 - 21:28

List Question

A converse to a lemma of Cesàro?

How do I evaluate $\sum_{n=1}^{\infty}\frac{n}{2n-1} - \frac{n+2}{2n+3}$?

How many real solutions does the equation $f(x) =0$ have, where $f(x) =\sum_{i=1}^{2020} \frac {i^2}{\left( x-i\right)} $

Alternative method to showing that $\sum_{r=-\infty}^{\infty}\frac{1}{64r^4+1}=\frac{\pi}{4}\frac{1+\sinh(\pi/2)}{\cosh(\pi/2)}$

If $S_{n,m}=\sum_{k=1}^{n} k^m =\sum_{j=0}^{m-1} A_{n,j}(m) S_{n,j},$ what are $A_{n,j}(m)$

$\sum_{n=1}^\infty\frac{n}{(2n-1)16^n}\binom{2n}{n}^2\left(\sum_{k=n}^\infty\frac{2^k}{k\binom{2k}{k}}\right)=1-\sqrt2+\log(1+\sqrt2).$

Prove that $\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{F_kF_{k+1}}=\frac{1}{\phi}$.

Partial sum estimate for $\sum_{p\leq x} \frac{1}{p^{1/2}}$

Does my odd proof for the Abel sum for $\eta(-2)$ work?

How to evaluate the following sum?

About the limit $\lim_{x\to 1^-} (1-x)\sum_{n\ge 0} a_n x^n=L$

Finding $\sum_{0 \le r <s \le n}~ (r+s){n \choose r}{n \choose s}$

What summation rule am I missing here?

Properties of $\sum _{l=0}^{\infty } \left( -1 \right) ^{l}{m+l-1\choose l} \left( 2 \,{\frac {l}{m}}+1 \right) ^{1-\nu}$

In search for a counterexample related to the Abel-Stolz theorem

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