I found this odd relationship, $x^2 = \sum_\limits{k = 0}^{x-1} (2k + 1)$.
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
64581
How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
118436
Identifying the series $\sum\limits_{k=-\infty}^{\infty} 2^k x^{2^k}$
17265
Intuition for why equations of the form $k^x=x^c$ are not solvable trivially?
26607
The idea behind the sum of powers of 2
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
114418
A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
139229
How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
19581
$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$
97720
Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
101011
An intriguing relation between two alternating series
146035
Proving $\sum_{x=0}^{n-1} \cos\left(k +x{2\pi\over n}\right) =\sum_{x=0}^{n-1} \sin\left(k +x{2\pi\over n}\right) =0. $
156367
How to prove that $\sum\limits_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)...(n+k)} = \frac{1}{kk!}$ for every $k\geqslant1$
137155
Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
130548
What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?