
Christopher J. answered 05/27/20
Berkeley Grad Math Tutor (algebra to calculus)
Taha:
Use an = (x-1)n/(3*n*(n+1)3)
an+1 = (x-1)n+1/(3*(n+1)*(n+2)3)
|an+1/an| = | (x-1) * (n/n+1) * ((n+1)/(n+2))3 |
as n goes to ∞ |an+1/an| goes to |x-1|
We need to find out on what interval |x-1|<1
Solve this inequality and don't forget to test the endpoints. Let me know if you need further help!