Principle of Mathematical Induction help?

Question

1+ 1/(1+2) + 1/(1+2+3) +....+ 1/(1+2+3...+n) = 2n/(n+1)

Answer 1

In a proof by induction, you must first prove the property works when n = 1, so plug in 1 and make sure you get the first term in your sequence.

You then prove that if it works for "n", then it must also work for "n + 1". So you're essentially given that
1 + 1/(1+2) + 1(1+2+3)+ ... 1/(1+2+3...+n) = 2n/(n+1)

You must prove that
1 + 1/(1+2) + 1(1+2+3)+ ... 1/(1+2+3...+n) + 1(1+2+3+...n+n+1) = 2(n+1)/((n+1)+1).

Chances are that you'll substitute all but the last term with the right side of your given and then attempt to simplify what remains.