The sum of the infinite series 1 3 + 3 3.7 + 5 3.7 . 11 + 7 3.7 . 11.15 + . . . . . . . is

Question

The sum of the infinite series 1 3 + 3 3.7 + 5 3.7 . 11 + 7 3.7 . 11.15 + . . . . . . . is, 1 2, 1 3, 1 6, 1 4

MARKS App · Accepted Answer

The n t h term of the series is t n = 2 n - 1 3.7 . 11 . - - - 4 n - 1 = 1 2 4 n - 1 - 1 3.7 . 11 . - - - 4 n - 1 = 1 2 1 3.7 . 11 . - - - 4 n - 5 - 1 3.7 . 11 . - - - 4 n - 1 = 1 2 u n - 1 - u n , n ≥ 2 Where, u n = 1 3.7 . 11 . - - - 4 n - 1 ⇒ S n = t 1 + ∑ k = 2 n t k = 1 3 + 1 2 u 1 - u 2 + u 2 - u 3 - - - + u n - 1 - u n = 1 3 + 1 2 u 1 - u n = 1 3 + 1 2 1 3 - u n ⇒ l i m n → ∞ S n = 1 3 + 1 6 - 1 2 l i m n → ∞ u n = 1 2 - 0 = 1 2

Search any question & find its solution

Looking for more such questions to practice?