So I am taking AP Calculus BC, and we are currently working on convergence and divergence of series. I came across the following problem in one of my homework assignments:
Here is the work I did to find the radius of convergence:
My teacher said I shouldn't have added 5 to each side, and left it at the highlighted step, meaning 6 would be the radius of convergence. I asked him why, and he said that the -5 is what centers the function.
Why is this the case? Does it have to do with Taylor Polynomials at all? If I do add 5, then isn't the radius still 6 because (11--1)/2 = 6
If any of you have an intuitive explanation for this, I would really appreciate it!