When is $\sum_{n=0}^{4}{x^n},~\text{where}~x\in \mathbb{N}>0$ square?
59782
Are there any $n$ for which $ n^4+n^3+n^2+n+1$ is a perfect square?
51509
How to show that $1 \over \sqrt{1 - 4x} $ generates $\sum_{n=0}^\infty \binom{2n}{n}x^n $
80440
Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
146333
Gaussian proof for the sum of squares?
69270
Questions about the powerseries $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n,d\in\mathbb{R},z\in\mathbb{C}$
135458
When is a sum of consecutive squares equal to a square?
38090
Partial sums of $nx^n$
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
133755
Is true that $\sum_{k=1}^n\frac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
146241
If $a \in \Bbb Z$ is the sum of two squares then $a$ can't be written in which of the following forms?
89279
If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
53443
Does $a_n \sim b_n$ imply $\sum_n a_n \sim \sum_n b_n$ for $a_n, b_n>0$?
147887
When do we have $ \lim_{n\to\infty}\sum_{k=1}^{n^2}\frac{n^{r-1}}{n^r+k^r}0$?
113891
The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
20142
$\sum a_n$ be convergent but not absolutely convergent, $\sum_{n=1}^{\infty} a_n=0$
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$