Prove $1+2+2^2+\dots+2^{n-1}=2^n-1$
52206
How to prove with double counting technique that $1+2+\dots+2^n=2^{n+1} -1$?
141909
Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
70625
Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
71014
Prove that 2(nC0+nC2...nC$\frac{(N-1)}{2}$=$2^n$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
87665
Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$