Question

Prove that $(1+2+3+\cdots+n)^2=1^3+2^3+3^3+\cdots+n^3$ $\forall n \in \mathbb{N}$.

score 827 · Answer 1 · 2026-04-15 18:59:16

827

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Prove that $(1+2+3+\cdots+n)^2=1^3+2^3+3^3+\cdots+n^3$ $\forall n \in \mathbb{N}$.

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score 79 · Answer 2 · 2026-04-11 02:12:07

79

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Trigonmetric sum of inverses

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score 166 · Answer 3 · 2026-04-15 08:06:46

166

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Evaluating $\sum_{n = 1}^{\infty} \frac{2}{2^{n}}$

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score 61 · Answer 4 · 2026-04-15 19:02:38

61

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To find the approximate solution of the series for large N

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score 520 · Answer 5 · 2026-04-12 10:20:35

520

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Difference between equals/approaches/approximate

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score 543 · Answer 6 · 2026-04-17 13:17:05

543

Views

If $A = \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\cdots+\frac{1}{\sqrt{999}}+\frac{1}{\sqrt{1000}}.$ Then $\lfloor A \rfloor$ is,

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score 139 · Answer 7 · 2026-04-13 18:06:21

139

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Evaluating $\sum\limits_{k=0}^n\cos(kx)$ and $\sum\limits_{k=0}^n\sin(kx)$ without Complex Numbers

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score 132 · Answer 8 · 2026-04-13 04:47:23

132

Views

Notation: $\sum\limits_{i=m}^n i$, with $m>n$.

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score 104 · Answer 9 · 2026-04-13 11:24:50

104

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Notation of sigmas

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score 222 · Answer 10 · 2026-04-17 09:56:31

222

Views

Reworking $\sum_{n \leq x} \frac{1}{n^s}$, where $n$ is relatively prime to some fixed $k$

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score 28.4k · Answer 11 · 2026-04-16 20:31:52

28.4k

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Is $\sum\frac{1}{\sqrt{n+1}}$ convergent or divergent?

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score 98 · Answer 12 · 2026-04-15 05:50:29

98

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How to do this limit: $\lim\limits_{n\to \infty}\large\frac{\sum_{k=1}^n k^p}{n^{p+1}}$?

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score 127 · Answer 13 · 2026-04-12 18:17:49

127

Views

Show that $\sum_{i=1}^{r} i^2 = \binom{r+1}{3} + \binom{r+2}{3}$ by finding generating function

Published on 12 Apr 2026 - 18:17

score 7.4k · Answer 14 · 2026-04-14 11:47:56

7.4k

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Sum of all triangle numbers

Published on 14 Apr 2026 - 11:47

score 57 · Answer 15 · 2026-04-12 13:28:27

57

Views

Is the series $\sum \frac{3 + \sin n}{n^2}$ convergent?

Published on 12 Apr 2026 - 13:28

List Question

Prove that $(1+2+3+\cdots+n)^2=1^3+2^3+3^3+\cdots+n^3$ $\forall n \in \mathbb{N}$.

Trigonmetric sum of inverses

Evaluating $\sum_{n = 1}^{\infty} \frac{2}{2^{n}}$

To find the approximate solution of the series for large N

Difference between equals/approaches/approximate

If $A = \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\cdots+\frac{1}{\sqrt{999}}+\frac{1}{\sqrt{1000}}.$ Then $\lfloor A \rfloor$ is,

Evaluating $\sum\limits_{k=0}^n\cos(kx)$ and $\sum\limits_{k=0}^n\sin(kx)$ without Complex Numbers

Notation: $\sum\limits_{i=m}^n i$, with $m>n$.

Notation of sigmas

Reworking $\sum_{n \leq x} \frac{1}{n^s}$, where $n$ is relatively prime to some fixed $k$

Is $\sum\frac{1}{\sqrt{n+1}}$ convergent or divergent?

How to do this limit: $\lim\limits_{n\to \infty}\large\frac{\sum_{k=1}^n k^p}{n^{p+1}}$?

Show that $\sum_{i=1}^{r} i^2 = \binom{r+1}{3} + \binom{r+2}{3}$ by finding generating function

Sum of all triangle numbers

Is the series $\sum \frac{3 + \sin n}{n^2}$ convergent?

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