Consider the expression

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

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

, where

n

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

6k-6(k-1)

and rewrite

T

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

T

in terms of

n

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

n=4

and (b)

n=7