Problem

Expand

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

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

S_n

of the first

n

integers. b. Hence find

a

and

b

such that

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

for all positive integers

n