SOLUTION: How can we prove the equation below? 1*1!+2*2!+3*3!+...+n*n!=(n+1)!-1

SOLUTION: How can we prove the equation below? 11!+22!+33!+...+nn!=(n+1)!-1

Question 957846: How can we prove the equation below?
1*1!+2*2!+3*3!+...+n*n!=(n+1)!-1
Answer by amarjeeth123(569) (Show Source): You can put this solution on YOUR website!
We can prove this equation using mathematical induction.
Let n=1
LHS=1*1!=1
RHS=2!-1=2-1=1
LHS=RHS
The equation holds true for n=1
We will assume that the equation holds true for n=k
1*1!+2*2!+.........+k*k!=(k+1)!-1......equation 1
For n=k+1 we have
LHS=1*1!+2*2!+.........+k*k!+(k+1)*(k+1)!
=(k+1)!-1+(k+1)*(k+1)!
=(k+1)!(k+1+1)-1
=(k+2)(k+1)!-1
=RHS
Therefore the equation holds true for all N.
RELATED QUESTIONS
Mathematical induction How can we prove that : (1 + 1 / 3) (1 + 5 / 4)(1 + 7 /... (answered by ikleyn)

prove that: 1+2+3+....+n =... (answered by ikleyn)

Prove 1 + 2^n < 3^n for n... (answered by checkley77)

Prove by induction n*1 + (n-1)*2 + (n-2)*3 + ... + 3*(n-2) + 2*(n-1) + 1*n =... (answered by ikleyn)

Prove by mathematical induction {{{1/(1*2) + 1/(2*3) + 1/(3*4)}}}+ ...+{{{1/n(n+1) =... (answered by Edwin McCravy)

Use induction to prove that... (answered by richard1234)

(n+1)! /... (answered by swincher4391)

USE PRINCIPLE OF MATHEMATICAL INDUCTION TO PROVE THE FORMULA 1(1!) + 2(2!) + 3(3!)... (answered by Edwin McCravy)

Use mathematical induction to prove the following. N^3 < or = (N+1)^2 ; N> or =... (answered by ikleyn)