Formalize a proof without words of the identity $(1 + 2 + \cdots + n)^2 = 1^3 + 2^3 + \cdots + n^3$
16812
Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
80216
Prove if $n \in \mathbb N$, then $\frac{1}{2!}+\cdots+\frac{n}{(n+1)!}=1-\frac{1}{(n+1)!}$
106965
How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?
141909
Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
65648
Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
86479
How to Prove with Mathematical Induction $3^n > n^2$
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
108688
An identity involving products of sums
36388
How to derive this Combinatorial identity
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
154722
How do I prove $2 \binom n2 + 4 \binom n4 + 6 \binom n6 + \cdots = n 2^{n-2}$
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$