Summation of an = 4 / (n + 1) (n + 3) sequence

Summation of an = 4 / (n + 1) (n + 3) sequence

If 4 / (n + 1) (n + 3) = 2 (1 / N + 1-1 / N + 3), then Sn = 2 (1 / 2 + 1 / 3-1 / N + 2-1 / N + 3) = 5 / 3-4n + 10 / (n + 2) (n + 3),