Preform a mathematical induction proof

Question

1•12+2•13+3•14+...+n(n+11)=n(n+1)(n+17) / 3

Answer 1

Base step: n = 1

1(1+11) = 1(1+1)(1+17)/3

12 = 12

This proves the base step.

Induction step: Assume the assertion true for n and check validity for n+1.

1.12 + ... + n(n+11) + (n+1)(n+12) = (using induction hypothesis)

n(n+1)(n+17)/3 + (n+1)(n+12) =

(n+1)(n(n+17)/3 + n+12) =

(n+1)(n² + 17n + 3n + 36)/3 =

(n+1)(n+2)(n+18)/3

The last line is the right hand side of the given assertion after replacing

n with n+1.

That proves the assertion.