Question

What is the sum of the infinite geometric series 1/2, 1/4, 1/8, 1/16? (a) (b) 2 (c) 1 (d) 2/3 (e) 3/2

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The sum of infinite GP series 1/2 , 1/4 , 1/8 , 1/16 ... is 1.

Step-by-step explanation:

• A sequence in which the ratio of two consecutive terms is constant is called Geometric Progression (GP) .
• A GP with a as first term and r as common ratio is a , ar , ar² , ar³ , ....
• The sum of an infinite GP with first term as a and common ratio, r is given by :

$S( \infty ) = \frac{a}{1 - r} \: \: \: \: \: \: \: where \: |r| < 1$

• The given GP is 1/2 , 1/4 , 1/8 , 1/16 ...
• First term, a of the given GP is 1/2.
• Common ratio, r is given by

$r = \frac{ \frac{1}{4} }{ \frac{1}{2} } = \frac{1}{2}$

• The sum of the infinite terms of GP is

$S( \infty ) = \frac{ \frac{1}{2} }{1 - \frac{1}{2} } \\ = \frac{ \frac{1}{2} }{ \frac{1}{2} } \\ = 1$

• Hence, the sum of given infinite GP is 1.