SOLUTION: Write the statements P1, Pk, PK+1 for the equation as if you were writing a proof by mathematical induction. You do not need to complete the proof. 1(1!)+2(2!)+...+n(n!)=(n+1)!

Algebra ->  Sequences-and-series -> SOLUTION: Write the statements P1, Pk, PK+1 for the equation as if you were writing a proof by mathematical induction. You do not need to complete the proof. 1(1!)+2(2!)+...+n(n!)=(n+1)!      Log On


   

Question 1137728: Write the statements P1, Pk, PK+1 for the equation as if you were writing a proof by
mathematical induction. You do not need to complete the proof.
1(1!)+2(2!)+...+n(n!)=(n+1)!-1
P1=?
Pk=?
Pk+1=?

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

P1 :       1*(1!) = (1+1)! - 1,  or, which is the same, 1 = 2! - 1.



Pk :       1(1!) + 2(2!) + . . . + k*(k!) = (k+1)!-1



P(k+1) :   1(1!) + 2(2!) + . . . + (k+1)*(k+1)! = (k+2)!-1

Answered.