Use induction to show the following for Fibonacci numbers:$ F_2 + F_4 + · · · + F_{2n} = F_{2n+1} − 1$ for every positive integer $n$
91068
Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
60712
Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
79657
Prove by induction $\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$ for $n\ge1$
57416
Fibonacci identity: $f_{n-1}f_{n+1} - f_{n}^2 = (-1)^n$
62556
Prove $3|n(n+1)(n+2)$ by induction
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
31245
How to prove that Fibonacci number is integer?
91889
Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
125297
Induction to prove $2n + 3 < 2^n$
40348
Proving by mathematical induction: $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1)$
115435
Induction: prove using congruences
48667
Proof by induction that fibonacci sequence are coprime
130093
Prove by Induction : $n < 2^n$
67886
How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence