Prove using induction that $1!\cdot 1+ 2!\cdot2+ 3!\cdot3+ ... +n!\cdot n = (n+1)!-1$
68848
How to simplify $\sum_{k=1}^nk\cdot k!$
134202
Proof by Induction - Math
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
108698
proof using the mathematical induction
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$
45914
Proving that $n!≤((n+1)/2)^n$ by induction
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
79847
proving of inequality $(n!)^2 \leq n^n\cdot n!\leq (2n!)$, where $n\in \mathbb{N}$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
88144
Induction Proof $n! < n^n$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
115435
Induction: prove using congruences