Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number
4855
How to show that this binomial sum satisfies the Fibonacci relation?
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
7003
Inductive proof of a formula for Fibonacci numbers
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
139625
Proof of a Fibonacci identity
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
64328
How to prove that the Binet formula gives the terms of the Fibonacci Sequence?
91068
Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
132486
Induction proof on Fibonacci sequence: $F(n-1) \cdot F(n+1) - F(n)^2 = (-1)^n$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
24407
How to prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$