Question

The sum of the series 1+3x+9x^2+27x^3+......infinity terms is a finite no. then
a)x>-1/3
b)x<-1/3
c)|x|<1/3
d)none of these​

Answer 1

Answer:

Option ( c ) = x < 1/3

Step-by-step explanation:

Given Series: 1 + 3x + 9x² + 27x³ + ... ∞

Analysing the pattern we get that it is multiplied by constant ratio 3x.

Therefore it forms a G.P

We know that, Sum of an infinite GP = a / ( 1 - r )

According to the question,

• a = 1
• r = 3x

Hence substituting the values we get,

⇒ Sum = 1 / ( 1 - 3x )

Since it is an infinite GP, r lies in the interval ( 0, 1 )

⇒ 0 < r < 1

⇒ r < 1

⇒ 3x < 1

⇒ x < 1/3

Hence Option ( c ) is the correct option.

Answer 2

Answer : x < 1/3

HOPE THIS WILL HELP YOU & HAVE A GOOD DAY