Proving the Fibonacci identity $\sum_{i=1}^n f_i^2=f_nf_{n+1}$ by induction
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
4855
How to show that this binomial sum satisfies the Fibonacci relation?
123427
Proving the sum of the first $n$ natural numbers by induction
57416
Fibonacci identity: $f_{n-1}f_{n+1} - f_{n}^2 = (-1)^n$
87941
Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
67527
Proof by Induction that $3^n ≥ 1+2^n$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
16177
Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
11407
Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
139426
Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction
101899
Proof By Induction of a Sum
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
116518
Proof by induction: $n$th Fibonacci number is at most $ 2^n$
62556
Prove $3|n(n+1)(n+2)$ by induction