Question

Find the radius of convergence, r, and interval, i, of convergence of the series [infinity] xn 11 n n = 1?

Answer 1

To find the radius of convergence (r) and interval of convergence (i) of a power series, apply the ratio or root test to find r, and then test the endpoints of the interval |x|

Step-by-step explanation:

The question seems to refer to the radius and interval of convergence of a power series, although the series itself is not written out explicitly in the provided text. Assuming we are dealing with a general power series ∑xn*11(n)^(n) from n=1 to infinity, we need to apply the ratio test or root test to determine the radius of convergence (r). The radius of convergence is given by the limit L = lim (n→∞) |a_(n+1)/a_n|, where a_n are the coefficients of the power series. If this limit exists, then r = 1/L. To find the interval of convergence (i), we need to test the endpoints of the interval |x|