trying to prove the following(adsbygoogle = window.adsbygoogle || []).push({});

1/1*2 + 1/2*3 + 1/3*4 +...+ 1/n(n+1) = n/n+1

Prove P(1) true: 1/1*2 = 1/1+1 = 1/2

Assume P(k) true: 1/2 + 1/6 + 1/12 + ... + 1/k(k+1) = k/(k+1)

trying to prove P(k+1) true:

step 1: 1/2 + 1/6 + 1/12 + ... + 1/k(k+1) + 1/(k+1)[(K+1)+1] = k+1/[(k+1) + 1]

step 2: k / (k+1) + 1/(k+1)[(K+1)+1] = k+1/[(k+1) + 1]

I keep ending up with k+1 / (k+2) ^2 on the left hand side.

I have not been able to figure out what I am doing wrong here.

Any ideas.

Thanks.

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# Proof by Induction

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