Mathematics

Problem

Consider the expression

T=\displaystyle \sum_{k=1}^{n}\bigl\{6k-6(k-1)\bigr\}

, where

n

is a positive integer. a. (i) Simplify the general term

6k-6(k-1)

and rewrite

T

as a summation of a constant term. b. (ii) Hence obtain a closed-form expression for

T

in terms of

n

. c. (iii) Verify your formula by directly expanding and adding the terms for (a)

n=4

and (b)

n=7