I don't even know how to solve the first problem.
I tried it this way.
Base step: P(0)
0*0 = 0 (0+1)! -1 =0
It is true
Inductive step: Assume P(k) is true then P(k+1) is also true.
P(k) = 1*1! + 2+2! +…………………………..+k*k! = (k+1)! -1 P(k+1) = 1*1! + 2+2! +…………………………..+(k+1)*(k+1)! = (k+2)!-1
From the first equation
(1*1! + 2+2! +…………………………..+ k*k!) +(k+1)*(k+1)! = (k+1)+1! -1
= (k+2)! -1
Is it correct?
