Summation $1-4x+9x^2-16x^3 + \cdots ?$
65653
Find a closed form of the series $\sum_{n=0}^{\infty} n^2x^n$
153409
Sum of $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{9}+\frac{1}{12}+\cdots$
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
101908
Solving summations of form $\sum_{i=0}^{\infty} i^kx^i$ without Differentiation and Integration
78632
Summation equation for $2^{x-1}$
29524
Formula for the sum $\sum_{i=2}^{n} \frac1{i^2-1}$
83229
Nested summations and their relation to binomial coefficients
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
78309
On an expansion of $(1+a+a^2+\cdots+a^n)^2$
147635
Find the sum $\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$
106888
Factorial identity $n!=1+(1-1/1!)n+(1-1/1!+1/2!)n(n-1)+\cdots$
113189
Find the sum of the series $1^2-2^2+3^2-4^2+...-(2n)^2$
97266
Summation by parts (finite calculus) of $\sum\limits_{i=0}^{n}i\cdot a^i$
30895
Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$
14306
What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$
155014
How to justify the definition of summation $s_n=\sum_{i=1}^n a_i=a_1+\cdots+a_n$?
124248
$1+\frac {1}{4}(1+\frac {1}{4}) +\frac {1}{9}(1+\frac {1}{4} +\frac {1}{9})+....$