Originally Posted by
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?