Prove the Binomial Expansion with Induction
66019
Revisited: Binomial Theorem: An Inductive Proof
65315
Showing $1+2+\cdots+n=\frac{n(n+1)}{2}$ by induction (stuck on inductive step)
10875
proof of binomial identity involving double sum
107335
Prove equality between binomial coefficients.
16347
Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
108596
Proof by induction for "sum-of"
88144
Induction Proof $n! < n^n$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
58481
Exclusion Inclusion Principle Induction Proof
63510
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
8609
Prove by induction that $n!>2^n$
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
40420
Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$