(a) Using the Ratio Test, or otherwise, determine the radius of convergence of the power series Σms (z – 24). n=1 State the test that you are using and justify all of your steps.
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- 6). Find the radius of convergence of the series. ∞ k = 1 2 · 4 · 6 2k (2k)! xk R = please show step by step clearlyFind a power series for the function, centered at C and determine the interval of convergence (function is h(x) and C = 0).h(x)=1/(1-5x) Also see the attached picture of the problem.Q3/ Find the radius of convergence and the interval of of the following series. .d 00 (x - 1)" n=1 n23n
- Find the radius and the interval of convergence of ∑∞n=1 (3^n*(2-x)^n)/(n+1)The function f(x) = (10x^2)/(1 / 2x)^2 is represented as a power series. Find c1, c2, c3, c4, c5 and find the radius of convergence R for the series.Find the radius of convergence and interval of convergence of Σ 1 to infinity (((-1)^n-1)(x-1)^n)/((2n-1)(2^n))
- (b) The series converges for every x in the half-open interval [−1, 1) but does not convergewhen x = 1. For a fixed x0 ∈ (−1, 1), explain how we can still use theWeierstrass M-Test to prove that f is continuous at x0.(a) find the series’ radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?Find the radius and interval of convergence of the series. X=∞ and n=0n!/2n + 1*x^n