What is the interval of convergence of the Taylor series of #f(x)=1/(1-x)#?
1 Answer
The Taylor Series of
which converges for
Explanation:
The general formula for the Taylor Series of
Let's find the general form for the
We can see the pattern emerging.
The formula appears to be
For simplicity, let's centre our Taylor Series at
Then
and the Taylor Series becomes:
Now that we have our series, let's use the ratio test to check for convergence.
Therefore the series converges for
Which can be expressed as
Let's check the endpoints of this interval.
Check
Check
So the final answer is: