1) If were rational, it would be of the form , where and are positive integers. Select an integer such that and . Use Taylor's theorem to show that

for some

Is this just the Taylor series about 0. and the end part is the Lagrange formula for the remainder?

2) Suppose that:

Show that is an integer

3) Show that

4) Conclude that is irrational

NOTE: I've posted my answer below. I just need someone to check whether I've done it correct. Thanks