Show that $1^3 + 2^3 + ... + n^3 = (n(n+1)/2)^2$ by induction
16812
Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
155562
Proving $\sum_{k=1}^nk^3 = \left(\sum_{k=1}^n k\right)^2$ using complete induction
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
130488
Prove by induction that $3\mid n^3 - n$
155897
Proof by induction - is this correct?
107824
Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$
106847
Proof that $n^3+2n$ is divisible by $3$
6165
Proof by Induction $n^2+n$ is even
52115
Show that $e^x > 1 + x + x^2/2! + \cdots + x^k/k!$ for $n \geq 0$, $x > 0$ by induction
8609
Prove by induction that $n!>2^n$
108698
proof using the mathematical induction
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
88292
Prove by induction that $\sum\limits_{i=1}^n \frac{1}{n+i} \leq \frac{3}{4}$