Which represents the series 1+1/3+1/9+1/27 using sigma notation

∑[1/(3^(n-1))] represents the series 1+1/3+1/9+1/27+1/81+1/243 using sigma notation. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

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swapnalimalwadeVT swapnalimalwadeVT · Answer 2 · 2022-04-08T10:45:10+02:00

The given series representation in sigma is \sum_{n=1}\frac{1}{3^{n-1}.

We have given that the series

1+1/3+1/9+1/27+1/81+1/243

That can be written as,

[tex]1+\frac{1}{3} +\frac{1}{3^2}+ \frac{1}{3^3} +\frac{1}{3^4}[/tex]

We use sigma notation

What is the meaning of sigma notation?

Sigma notation indicate that the sum of the nth terms.

Here n=1 then [tex]a_1=1[/tex]

[tex]n=2,a_2=\frac{1}{3}[/tex]

[tex]n=3,a_3=\frac{1}{3^2} \\\\n=4,a_4=\frac{1}{3^3}[/tex]

[tex]for nth term ,a_n=\frac{1}{3^{n-1} }[/tex]

So from above we get,

[tex]\sum_{n=1}\frac{1}{3^{n-1}}[/tex]

So the given series representation in sigma is

\sum_{n=1}\frac{1}{3^{n-1}}.

To learn more about the series visit:

https://brainly.com/question/25870256