Question

27,9,3,1,1/3,1/9....Write the sigma notation for the infinite series. ________________

Answer 1

Given

Series,

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

Find

Write the sigma notation for the infinite series.

Step-by-step explanation

as we see the given series is a geometric series .

here , a = 27

common ratio , r = 9/27 = 1/3

so ,

`\begin{gathered} \sum_{n\mathop{=}1}^(\infty)ar^(n-1) \\ \\ \sum_{n\mathop{=}1}^(\infty)(27)((1)/(3))^(n-1) \\ \\ \sum_{n\mathop{=}1}^(\infty)((1)/(3))^(-3)((1)/(3))^(n-1) \\ \\ \sum_{n\mathop{=}1}^(\infty)((1)/(3))^(n-4) \end{gathered}`

Final Answer

Hence , the sigma notation for the infinite series is

`\sum_{n\mathop{=}1}^(\infty)((1)/(3))^(n-4)`