If the set of natural numbers is partitioned into subsets `S_1={1},S_2={2,3},S_3={4,5,6}` and so on then find the sum of the terms in `S_(50)dot`

If N, the set of natural numbers is partitionaed into groups S_(1)={1},S_(2)={2,3},S_(3)={4,5,6,7},S_(4)={8,9,10,11,12,13,14,15},"....", find the sum of the numbers n C_(50).

If S_(1)={2},S_(2)={3,6},S_(3)={4,8,16},S_(4)={5,10,20,40} then the sum of numbers in the set S_(15) is