This is an exercise in my book that I can't figure out. And there's no answer sheet for it so I don't know if I did it right.

an = 1/n+1 - 1/n+2

I got these as the first terms of the sequence:

a1 = 1/6

a2 = 1/12

a3 = 1/20

a4 = 1/30

Based on those, I got these as the first partial sums of the sequence:

S1 = 1/6

S2 = 1/4

S3 = 3/10

S4 = 1/3

I feel the partial sums are wrong, and I can't figure out the Nth partial sum of the sequence (Sn = ?).

Any help or pointer would be greatly appreciated.

Thank you.