Question

prove using induction:
1*1!+2*2!...n*n!=(n+1)!-1

Answer 1

p(k)=1*1!+2*2!....k*k!=(k+1)!-1
p(k+1)=(k+1)!+1+(k+1)!*(k+1)= (k+2)!-1

Answer 2

but then i get stuck... i dont know what to do.
on the left side i can take out (k+1)! but i dont see how that helps me