Question

36. Find the sum of the infinite geometric series if it exists.

1+\frac{3}{2}+\frac{9}{4}+\frac{27}{8}+\cdots

Answer 1

`=2* \left( (3)/(2) \right)^(n+1) -2`

Explanation:

`1+(3)/(2) +(9)/(4) +(27)/(8) +\cdots`

`=1+\left( (3)/(2) \right)^(1) +\left( (3)/(2) \right)^(2) +\cdots +((3)/(2))^n`

`=(1-\left( (3)/(2) \right)^(n+1) )/(1-(3)/(2) )`

`=-2* \left( 1-\left( (3)/(2) \right)^(n+1) \right)`

`=2* \left( \left( (3)/(2) \right)^(n+1) -1\right)`