sequences and series help? URGENT!!!

Question

Find the sum of 1 + 3/2 + 9/4 + …, if it exists.

 

a) 4.75

 

b) -2

 

c) 5

 

d) no sum

 

Answer 1

This is a geometric progression series since each term after the first is  r =3/2 the previous term.

The infinite sum of this geometric progression series exists when |r| < 1

Since r > 1, the series has no finite sum.

Answer 2

You have a series here where the terms are

 

∞  3ⁱ

∑  ---

^_i=0  2ⁱ

 

This can also be written as

 

∞ 
∑     (3/2)ⁱ
i=0 

 

Since r= 3/2, the common ratio is greater than 1, the terms of the series get larger and larger and the series has no sum.