Expand , then write the expansion again underneath with the terms in reverse…

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

Expand

\sum_{k=1}^{n}k

, then write the expansion again underneath with the terms in reverse order. (1) Add the terms vertically, and hence write an expression for the sum

S_n

of the first

n

integers. (2) Hence find

a

and

b

such that

\sum_{k=1}^{n}(ak+b)=8n^2+11n

for all positive integers

n