Let S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + … + 1 + 2 + … , + n 1 3 + 2 3 + … n 3 . If 100 S n = n , then n is equal to:

Step-by-step solution

Given, S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + … + 1 + 2 + … + n 1 3 + 2 3 + … + n 3 T n = n n + 1 2 n n + 1 2 2 T n = 2 n n + 1 = 2 1 n - 1 n + 1 S n = 2 ∑ n = 1 n 1 n - 1 n + 1 S n = 2 1 - 1 n + 1 = 2 n n + 1 Given, 100 S n = n ⇒ 100 × 2 n n + 1 = n n + 1 = 200 n = 199