Question

Find the sum of the following infinite series.1/3−2/21+4/147−8/1029+···

Answer 1

Given:

The series is 1/3−2/21+4/147−8/1029+··

Step-by-step explanation:

For the given series, the first term is,

`a=(1)/(3)`

The common ratio is,

`\begin{gathered} r=(-(2)/(21))/((1)/(3)) \\ =-(2)/(21)\cdot(3)/(1) \\ =-(2)/(7) \end{gathered}`

The formula for the sum of infinite series is,

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

Substitute the values in the formula to determine the sum of infinite series.

`\begin{gathered} S_(\infty)=((1)/(3))/(1-(-(2)/(7))) \\ =((1)/(3))/((9)/(7)) \\ =(1)/(3)*(7)/(9) \\ =(7)/(27) \end{gathered}`

Answer: 7/27