Fibonacci sequence: Prove the formula $f_{2n+1}=f_{n+1}^2 + f_n^2$
60712
Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
121167
explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$
57416
Fibonacci identity: $f_{n-1}f_{n+1} - f_{n}^2 = (-1)^n$
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
91068
Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction
105882
Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
133150
Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$
112948
Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
15164
Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
50827
How to write the Fibonacci Sequence?
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$