Proof involving Fibonacci number and binomial coefficient
4855
How to show that this binomial sum satisfies the Fibonacci relation?
157601
Proof a formula of the Fibonacci sequence with induction
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
155995
Fibonacci proof question: $f_{n+1}f_{n-1}-f_n^2=(-1)^n$
8806
Summation of binomial coefficients
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
116518
Proof by induction: $n$th Fibonacci number is at most $ 2^n$
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
79124
Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
106183
Proof by Induction: Alternating Sum of Fibonacci Numbers
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
9046
Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
14784
Inductive proof of the closed formula for the Fibonacci sequence
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
31245
How to prove that Fibonacci number is integer?
91914
Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.