Why is $\sum_{i=0}^{w-1}{2^i} = 2^w - 1$?
26607
The idea behind the sum of powers of 2
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
130548
What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
57894
In a proof of the Sherman-Morrison formula why does $(I+wv^T)^{-1}=I-\frac{wv^T}{1+v^Tw}$
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
146533
Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
69131
Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?
69270
Questions about the powerseries $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n,d\in\mathbb{R},z\in\mathbb{C}$
77517
Why is this sum a representation of e?
14487
Does $\sum_{n=2}^\infty (n\ln n)^{-1}$ diverge?
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?