My question states: Use the identity 1/( -1)= 1/2(1/(k-1)-1/(k+1)) to evaluate k=1 to n 1/( -1)

so I have 1/2( k=1 to n 1/(k-1)-1/(k+1)). I feel like from here i'm supposed to manipulate the 1/k-1 to some how get it so I can have a_j =1/(j+1) and then replace all the 1/k+1 by a_j..however i'm not exactly sure how to go about this. Would it turn into 1/a_j-2 -a_j ?? if so what do i do from here?