I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also checking the end points).

An automatic response to a power series of this type is to use the ratio test. In the ratio test, you want to look at the limit as n goes to infinity of the absolute value of a_n+1 / a_n:
lim |a_n+1|
n->inf --------
| ...

Solution Summary

This provides the steps to find the interval of convergence (also checking the end points).

... According to the hint given, the convergence of should have been uniform we are ... Suppose f_n is defined on a finite interval I and 〖f'〗_n is continuous on I ...

... 3. Find the open interval of convergence and test the endpoints for absolute and conditional convergence. a) ∑[∞/ n=1] ((x+1)^n) / ((3^n)(n)). ...

... on page 39 as the set of all functions continuous on interval [a,b ... With metric defined by equation (0.1) it means simultaneous (uniform) convergence for each ...

... as n tending to infinity for the absolute value of this ratio, we get as for any So the radius of convergence is zero, and there's no interval of convergence. ...

... extends our understanding of the convergence of their ... can produce 90%, 99%, 99.9%, confidence intervals for the ... The width of the confidence interval gives us ...

... proof, the definitions of cofinite set, filter, filter generated by a set, convergence of a ... The example given in (b) is X = (0, 1), the open interval of the ...

... Precisely, the rate of convergence is given by the largest number p (often an integer) such that ... bisect(f,a,b,tol) that finds a root r of f in the interval [a,b ...