Question

Write each series as a summation in sigma notation

Answer 1

`\displaystyle\sum_(i=1)^4{15\left((-1)/(5)\right)^(i-1)}`

Explanation:

You want the sum 15 -3 +3/5 -3/25 written using sigma notation.

Sigma notation

Sigma notation makes use of the expression for a general term, using the term index number as a variable. Here the terms are considered to be 1 through 4, so the number above the sigma symbol (∑) is 4.

General term

The series is a geometric series with first term 15 and common ratio -1/5. The general term is written as ...

an = a1 +r^(n-1)

where a1 is the first term, r is the common ratio, and n is the term index.

For our sigma expression, we will use i as the term index, so we have ...

`\boxed{\displaystyle\sum_(i=1)^4{15\left((-1)/(5)\right)^(i-1)}}`

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Additional comment

The factor 15 can be brought outside the sigma expression. The sum of these four terms is 12.48, or 12 12/25.

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