Check if this is correct!

Sorry, a bit of a click bait title with the capitals. Can someone check if this explanation is correct? Maths question -80% of those who clicked lost at this point. Thanks

Posted from TSR Mobile

That looks fine. However, the proof would have worked much more neatly if you used $2n$ and $2n+1$ as your consecutive numbers. You'd end up with $4(2n^2+n) + 1$, which is more explicit in showing the required result.

Ahh thank you! One question I have. Is it better to use 2n and 2n+1 as the consecutive numbers as opposed to n and n+1 in proof questions? Or was it only better in this scenario?

Posted from TSR Mobile

Ahh thank you! One question I have. Is it better to use 2n and 2n+1 as the consecutive numbers as opposed to n and n+1 in proof questions? Or was it only better in this scenario?

Posted from TSR Mobile

Hmm, it depends on what you're trying to show it is a multiple of. Here we wanted a multiple of 4, so I realised that because we have squares, we may as well use $2n$, as when squared, that'll give us the factor of 4 we want.

However, using $2n$ and $2n+1$ will result in larger coefficients, which given the nature of questions you're likely to get, will probably make the proofs come out a lot easier / nicer.