Question

find sum of geometric series Q = 2q + q/3 + q/9 + q/27 ....... infinity

Answer 1

The given geometric series:

Q =  $q+\dfrac{q}{3}+\dfrac{q}{9}+\dfrac{q}{27}+........ \infty$

Here, first term (a) = q and common ratio (r) = $\dfrac{\dfrac{q}{3} }{q} =\dfrac{1}{3}$

We have to find, the sum of the infinite geometric series, Q.

Solution:

We know that,

The sum of the infinite geometric series = $\dfrac{a}{1-r}$

Q =  $q+\dfrac{q}{3}+\dfrac{q}{9}+\dfrac{q}{27}+........ \infty$

Q = $\dfrac{q}{1-\dfrac{1}{3}}$

⇒ Q = $\dfrac{q}{\dfrac{2}{3}}$

⇒ Q = $\dfrac{3q}{2}$

Thus, the sum of the infinite geometric series, Q = $\dfrac{3q}{2}$.

Answer 2

Given : Geometric series Q =  2q + q/3 + q/9 + q/27 ...   infinity  

To Find : Sum

Solution:

2q + q/3 + q/9 + q/27 ...   infinity  

= q + q + q/3 + q/9 + q/27 ...   infinity  

= q + (q + q/3 + q/9 + q/27 ...   infinity  )

a =  q

r = (q/3)/ q  =  1/3  

S = a/(1 - r)   =  q/(1 - 1/3)

= 3q/2

Q = q + 3q/2

=> Q = 5q/2

Hence Sum is 5q/2

if Question is

q + q/3 + q/9 + q/27 ...   infinity  

Then sum is 3q/2

Learn More:

In an infinite g.P. Each term is equal to three times the sum of all the ...

brainly.in/question/9079152

In an infinite gp series the first term is p and infinite sum is s then p ...

brainly.in/question/12999165