Question

Express the series using sigma notation. -8 + 4 - 2 + 1.

Answer 1

`\bf -8~~,~~\stackrel{-8\left( -(1)/(2) \right)}{4}~~,~~\stackrel{4\left( -(1)/(2) \right)}{-2}~~,~~\stackrel{-2\left( -(1)/(2) \right)}{1}~\hspace{8em}{\displaystyle\sum\limits_(i=1)^(4)}~-8\left( -(1)/(2) \right)^(i-1)`

Answer 2

-12

Explanation:

I believe you want the "sum of the series," because that's what you get from "sigma notation." Two cases here: infinite series and partial series.

If you wish to find the sum of the infinite series whose first term is a = -8 and whose common ratio is r = (-1/2), use the formula

a

sum of infinite series = -------------

1 - r

which here comes to

-8

sum of infinite series = ----------------- = -8/(3/2) = -12

1 - (-1/2)