Question

The sum to n terms of the series 1/1 - 1/4 + 1/(1 + 3) - 1/4 + 1/(1 + 3 + 5) - 1/4 + ... ∞

(a)  2n/2n + 1

(b)  4n/2n + 1

(c)  2/2n + 1

(d)  none

Answer 1

Correct option (b)  4n/2n + 1

Explanation:

T_n  = 1/(1 + 3 + 5 + .... + n terms) = 1/n² - 1/4

T_n = 2(1/2n - 1 - 1/2n + 1)

Adding, S_n = T₁ + T₂ +.............+ T_n = 2(1 - 1/2n + 1)

= 4n/2n + 1