Question

The sum of the series 1/1.3 + 2/13.5 + 3/1.3.5.7 + ...... ∞ is 

(a)  1

(b)  1/2 

(c)  3/2

(d)  None

Answer 1

Correct option (b) 1/2

Explanation:

T_n = n/1.3.5......(2n - 1)(2n + 1)

T₁  = 1/2(1/1 - 1/1.3)

T₂ = 1/2(1/1.3 - 1/1.3.5)

∴  S_∞ = 1/2(1 - 0) = 1/2