I am to prove the following equation by induction:

(1/2)+(1/6)+(1/12)+...+1/n(n+1)=n/(n+1)

so far I have the base case= 1

Assume this is true for n=k

(1/2)+(1/6)+(1/12)+...+1/k(k+1)=k/(k+1)

now I want to assume this is true for n=k+1

(1/2)+(1/6)+(1/12)+...+1/(k+1)(k+2)=(k+1)/(k+2)

This is where I am stuck...am I placing (k+1) in the correct places?