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**renolovexoxo** Prove 1/1(2)+2/2(3)+...+1/n(n+1)=n/n+1

I've been using induction to prove this.

For the base case I got: 1/1(2)=1/2

Then I go on and get a little more stuck:

Assume 1/1(2)+2/2(3)+...+1/n(n+1)=n/n+1 for all n in N. Want to show that 1/1(2)+2/2(3)+...+1/n(n+1)+1/(n+1)(n+2)=(n+1)/(n+1)+1

I simplified it using the assumption

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

Then when I tried to simplify I keep getting something that isn't an equality. Have I done something wrong so far?