consider the following series

infinity ∑ n=1 x^n /5^n

find the value of x for which the series converges

answer in interval notation

2) find the sum of the series for those value of x. Write the formula in terms of x.

Sum=

Question

consider the following series

infinity ∑ n=1 x^n /5^n

find the value of x for which the series converges

answer in interval notation


2) find the sum of the series for those value of x. Write the formula in terms of x. 

Sum=

anonymous · Answer

http://www.wolframalpha.com/input/?i=sum+%28x^n%29%2F%285^n%29+n%3D0+to+infinity

anonymous · Answer

How do I do it by steps?

anonymous · Answer

apply the ratio test, and force the ratio to be less than 1.

anonymous · Answer

Hi, how do I find  the value of x for which the series converges

answer in interval notation

anonymous · Answer

I'm still a bit confused...

anonymous · Answer

$$\left|\frac{a_{n+1}}{a_n}\right|<1$$

anonymous · Answer

Where $$a_n=\frac{x^n}{5^n}$$

anonymous · Answer

Thats how you do these problems in general.  Although for this particular problem, you can use the fact that:$$\frac{x^n}{5^n}=\left(\frac{x}{5}\right)^n$$so your series is a geometric series, which only converges is the common ratio is less than 1.