How would you prove that via induction? $\sum_{k=1}^{n}k! \cdot k= (n+1)! -1$
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
81136
Prove by induction that... $1+3+5+7+...+(2n+1)=(n+1)^2$ for every $n \in \mathbb N$
151646
Prove by induction that $\sum_{i=1}^{n} i \cdot 2^i = (n-1) \cdot 2^{n+1} +2$. Help finding my mistake
108596
Proof by induction for "sum-of"
16347
Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$
47827
Prove that $\sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$
122534
Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
62177
Prove that: $2^n < n!$ Using Induction
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
88144
Induction Proof $n! < n^n$
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
86896
Prove by induction. How do I prove $\sum\limits_{i=0}^n2^i=2^{n+1}-1$ with induction?