What is the sum of the following infinite series? 2 + 1 + 1/2 + 1/4 + 1/8...

Question

a 3

b 6

c 5

d 4

Answer 1

for n=0,1,2,...,infinity

 

the general term of the series is:

 

2^(1-n) = 2^1*2^(-n))

 

            = 2* (1/2)^n

 

  The leading coefficient is 2 and the common ratio is (1/2)

 

  So the series converges to 2 /  ( 1 - 1/2) = 2 / (1/2) = 2*2 - 4

 

The answer is D