Infinite Sum using $x^{-x}$
74454
Sophomore's dream: $\int_0^{1} x^{-x} \; dx = \sum_{n=1}^\infty n^{-n}$
725
proof of $\sum_{n=1}^\infty n \cdot x^n= \frac{x}{(x-1)^2}$
51509
How to show that $1 \over \sqrt{1 - 4x} $ generates $\sum_{n=0}^\infty \binom{2n}{n}x^n $
107976
Find a closed formula for $\sum_{n=1}^\infty nx^{n-1}$
86603
Infinite square-rooting
157075
Infinite summation 21
81124
Infinite product problem: $\sum p_n0$
135927
Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
8676
Is there any "superlogarithm" or something to solve $x^x$?
17214
Transfinite series: Uncountable sums
122236
How to compute the series: $\sum_{n=0}^{\infty} (-1)^{n-1}\binom{1/2}{n}$
125876
Sum and Product of Infinite Radicals
98933
Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
37771
Sum of a power series $n x^n$
86194
Infinite series with the binomial coefficient
145582
$\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test?
130548
What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?