Using the Fibonacci sequence and deduction to prove...
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
91889
Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.
61671
Discrete Math: Writing Proofs
5801
Combinatorial proof help
65168
Proof of sequence inequality
106502
Prove by induction that for the Fibonacci numbers $F(n)$ with $n \ge 6$, $F(n) \ge 2^{n/2}$
93022
Prove that a given recursion sequence converges
116518
Proof by induction: $n$th Fibonacci number is at most $ 2^n$
24256
General term for fibonacci sequence
131400
Solution check: Let $f_n$ be fibonacci numbers. Prove: $\sum_{k=0}^{n-1} \binom{n+k}{2k+1} = f_{2n-1}$ and $\sum_{k=0}^n \binom{n+k}{2k} = f_{2n}$
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
48610
Fibonacci Numbers Proof: $ f_n = \binom n0 + \binom{n-1}1 +\dots+ \binom{n-k}k$
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
65983
Combinatorial proof of binomial coefficient summation identity
21137
Recurrence relation, induction and Fibonacci numbers
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Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$
44622
If $F_n$ is the Fibonacci sequence, show that $F_n < \left(\frac 74\right)^n$ for $n\geq 1.$