Question

For what values of x will the sum of the series be a finite value?

7-7(x)+7(x^2)-7(x^3)+7(x^4)-...

Answer 1

7(1-x+x^2-x^3-...)
Inside looks geometric. r=-x

Answer 2

so for what values of x will the sum of the series be finite?
x > 1
x < -1 , x > 1
-1 < x < 1
x < 1

Answer 3

For abs(r)<1

Answer 4

so -1<x<1 right?

Answer 5

how do I Find the value of the infinite series for x in the interval?

Answer 6

There is a well known closed form of the sum of an infinite geometric series.

Answer 7

a/(1-r)?

Answer 8

Yup