How do you find the power series for #f(x)=int tln(1-t)dt# from [0,x] and determine its radius of convergence?
1 Answer
Explanation:
We have:
Focus on the function:
We know that:
where the integrand function is the sum of the geometric series:
then we can integrate term by term, and we have:
and mutiplying by x term by term:
We can substitute this expression in the original integral and integrate again term by term:
To determine the radius of convergence we can then use the ratio test:
and the series is absolutely convergent for