Question

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

Answer 1

Answer:

Option (4)

Step-by-step explanation:

Given sequence is,

$1+\frac{3}{2}+\frac{9}{4}..........$

We can rewrite this sequence as,

$1+\frac{3}{2}+(\frac{3}{2})^2.............$

There is a common ratio between the successive term and the previous term,

r = $\frac{\frac{3}{2}}{1}$

r = $\frac{3}{2}$

Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.

Since sum of infinite geometric sequence is represented by the formula,

$S_{n}=\frac{a}{1-r}$  , when r < 1

where 'a' = first term of the sequence

r = common ratio

Since common ratio of the given infinite series is greater than 1 which makes the series divergent.

Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.

Option (4) will be the answer.