The sum of 50 terms of the series 3 + 7 + 13 + 21 + 31 + 43 + . . . . . is equal to S 50 , then the value of S 50 12500 is

Step-by-step solution

Let, S = 3 + 7 + 13 + 21 + 31 + 43 + . . . . . + T n S =       3 + 7 + 13 + 21 + 31 + . . . . . + T n - 1 + T n Subtracting both the equations, we get, 0 = 3 + 4 + 6 + 8 + 10 + . . . . . . . . + T n - T n - 1 - T n ⇒ T n = 3 + 4 + 6 + 8 + 10 + . . . . . . . . n - 1 t e r m s = 3 + n - 1 2 8 + n - 2 2 = 3 + n - 1 4 + n - 2 = 3 + n - 1 n + 2 = 3 + n 2 + n - 2 = n 2 + n + 1 S n = Σ T n = Σ n 2 + Σ n + Σ 1 = n n + 1 2 n + 1 6 + n n + 1 2 + n If n = 50 , S 50 = 50 × 51 &#215