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Proof by Induction

Hi, im trying to prove the attached series by mathematical induction. This is what I have done so far:

(check insert)

I think I have gone wrong somewhere, and also where do I go from here? Any help would be appreciated. Thankyou! :colondollar:

proof by induction.png1.0KB

proof by induction 2.png4.6KB

Reply 1

Zuzuzu

\displaystyle LHS = \frac{n}{n+1} + \frac{1}{(n+1)(n+2)}

Reply 2

TheMagicMan

Original post by rede121

There is a more elegant direct method called the method of differences which you can look up. I'm not really sure what you are doing in your induction, but the LHS is explicable as the sum of the k+1th terms and the sum of the first k terms: