Why is $(1+2+3+4+...+n)^2$ equal to $1^3+2^3+3^3...+n^3$?
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
103572
Does $\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}a_{mn}^3=\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{mn}^3$ occur here?
134311
How to determine equation for $\sum_{k=1}^n k^3$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
152588
Expression for $n+n(n-1)+n(n-1)(n-2)+...+n!$
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
113189
Find the sum of the series $1^2-2^2+3^2-4^2+...-(2n)^2$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
32355
How to find the sum of the sequence $\frac{1}{1+1^2+1^4} +\frac{2}{1+2^2+2^4} +\frac{3}{1+3^2+3^4}+.....$
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
2675
Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
89758
Is there a formula for $(1+i)^n+(1-i)^n$?
48211
When is $(a+b)^n \equiv a^n+b^n$?
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$