Question

27,9,3,1,1/3,1/9......Find the sum of the infinite series. ________________

Answer 1

Given the following series:

`27,9,3,1,(1)/(3),(1)/(9),.....`

The given series is a geometeric sequence

the first term = 27

And the common differnce = 1/3

we will use the following formula to find sum of the series as the number of terms tends to infinite:

`S_(\infty)=(a)/(1-r)`

substitute a = 27, and r = 1/3

`S_(\infty)=(27)/(1-(1)/(3))=(27)/((2)/(3))=40(1)/(2)=40.5`

So, the answer will be, the sum of the infinite series = 40.5