If the sum of the first 15 terms of the series 3 4 3 + 1 1 2 3 + 2 1 4 3 + 3 3 + 3 3 4 3 + … is equal to 225 K , then K is equal to :

Step-by-step solution

Given series, 3 4 3 + 6 4 3 + 9 4 3 + 12 4 3 + 15 4 3 + … 15 terms = 3 4 3 1 3 + 2 3 + 3 3 + … + 15 3 = 27 64 15 × 16 2 2       ∵ ∑ n = 1 n = n n 3 = n n + 1 2 2 = 27 64 × 225 × 64 1 = 27 × 225 Since, given 225 K = 27 × 225 ⇒ K = 27