The sum of the series 11.2−12.3+13.4−…..∞ | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

The sum of the series 11.2−12.3+13.4−…..∞

A

(A) 2loge 2 + 1

B

(B) 2loge 2

C

(C) 2loge 2 – 1

D

(D) loge 2 – 1

Answer

(C) 2loge 2 – 1

Explanation

Solution

Explanation:
s=11.2−12.3+13.4……∞=(11−12)−(12−13)+(13−14)=11−12−12+13+13−14−14+15…=11−22+23−24+25−…=2[11−12+13−14+15…]−1=2log⁡2−1