Prove by induction that $\sum_{k=0}^n k\cdot k! = (n+1)!-1$
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
106888
Factorial identity $n!=1+(1-1/1!)n+(1-1/1!+1/2!)n(n-1)+\cdots$
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
101899
Proof By Induction of a Sum
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
26901
induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$
3043
Prove $n!>2^n$ for $n\geq4$ using induction.
123853
Finding a formula for $1+\sum_{j=1}^n(j!)\cdot j$ using induction
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
124584
How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
47827
Prove that $\sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$