Question

Find the sum of the geometric series.

a
b
c
d

Answer 1

B.
`4√(3)-6`

Explanation:

We have,

The first term of the series,
`a=√(3)`.

The common difference is given by,
`r=((-3)/(2))/(√(3))` i.e.
`r=(-√(3))/(2)`.

Since, the given series is an infinite series, then,

Sum of an infinite series =
`(a)/(1-r)`

i.e. Sum the series =
`(√(3))/(1+(√(3))/(2))`

i.e. Sum the series =
`(2√(3))/(2+√(3))`

i.e. Sum the series =
`(2√(3))/(2+√(3))* (2-√(3))/(2-√(3))`

i.e. Sum the series =
`(2√(3)* (2-√(3)))/(4-3)`

i.e. Sum the series =
`4√(3)-6`

Thus, the sum of the series is
`4√(3)-6`.