How do you find the power series for #f'(x)# and #int f(t)dt# from [0,x] given the function #f(x)=Sigma sqrtnsqrt(n+1)x^n# from #n=[1,oo)#?
1 Answer
Dec 21, 2017
for
Explanation:
Consider for
using the ratio test we have:
so:
and we can conclude that the series is convergent for
Inside the interval of convergence we can integrate and differentiate the series term by term, so if:
then: