Review question

# Can we sum the first $2n$ terms of $1^2-3^2+5^2-7^2+\cdots$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5416

## Suggestion

By bracketing the terms in pairs, or otherwise, find the sum of $2n$ terms of the series $1^2-3^2+5^2-7^2+\cdots.$

Hence show that the sum of $2n+1$ terms is $8n^2+8n+1$.

Can we find an expression for a general term in the series?

What is the sign of the $2k^{th}$ term?

Can we find expressions for the two terms in the $k^{th}$ pair?

Can we factorise $a^2-b^2$?

Can we check our formula by substituting in a couple of values for $n$?