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

## Question

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 $8n^2+8n+1$.