Prove 1 + a + a^2 + a^3 + .... a^n-1 = 1-a^n/1-a by mathematical induction
58633
Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
108596
Proof by induction for "sum-of"
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
18301
Proof by Induction involving Inequality and Factorials as denominators
16177
Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
30783
Prove inequality $n<3^n$ using mathematical induction
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$
40348
Proving by mathematical induction: $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1)$
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
128309
Use Mathematical Induction to prove that $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$
134202
Proof by Induction - Math
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
41784
Prove using mathematical induction that $n < 3 ^n$ for all positive integers n.
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$