Each of the following represent an infinite geometric series. For what values of x will each series be convergent?
a) 5+5x+5x^2+5x^3+...
b)1+ x/3 + x^2/9=x^3/27+...
and can someone please explain the difference between converging and diverging series?
Math infinite geometric series question?
2018-09-30 3:29 am
回答 (2)
2018-09-30 4:40 am
A geometric series converges if -1 < r < 1.
(a) r = x, so the series converges if -1 < x < 1
(b) r = x/3, so the series converges if -3 < x < 3
Your textbook can explain why. If you can't afford a textbook, there's always Wikipedia. https://en.wikipedia.org/wiki/Convergent_series
(a) r = x, so the series converges if -1 < x < 1
(b) r = x/3, so the series converges if -3 < x < 3
Your textbook can explain why. If you can't afford a textbook, there's always Wikipedia. https://en.wikipedia.org/wiki/Convergent_series
2018-09-30 3:41 am
Converging means that as you keep adding terms from the infinite sum it gets closer and closer to a value, a diverging series won't.
So in geometric series if the terms go to 0 it will converge.
What values of x goes to 0 when n goes to infinity 5x^n?
What values of x goes to 0 when n goes to infinity (x/3)^n?
Answer is |x| < 1, |x/3| < 1
So in geometric series if the terms go to 0 it will converge.
What values of x goes to 0 when n goes to infinity 5x^n?
What values of x goes to 0 when n goes to infinity (x/3)^n?
Answer is |x| < 1, |x/3| < 1
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