How to derive the formula for the sum of the first $n$ odd numbers: $n^2=\sum_{k=1}^n(2k-1).$
71736
I found this odd relationship, $x^2 = \sum_\limits{k = 0}^{x-1} (2k + 1)$.
122005
Can $n(n+1)2^{n-2} = \sum_{i=1}^{n} i^2 \binom{n}{i}$ be derived from the binomial theorem?
114418
A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
3798
Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
134311
How to determine equation for $\sum_{k=1}^n k^3$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
136066
Find the sum $\sum _{n=1}^{\infty }\left(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}\right)$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
61547
Derive an explicit formula for a power series $\sum_{n=1}^\infty n^2x^n$
50050
A formula for the power sums: $1^n+2^n+\dotsc +k^n=\,$?
122534
Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
19581
$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$