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 \(n\)?
