Question

What 2n 7. Determine the radius and interval of convergence of the power series function has this power series as its Taylor series at 07 (10) 27-1 8. Consider the rational function (x) Find the Taylor series at 0 of (2) and determine its radius and interval of convergence. (10) 2-1

Answer 1

Solution :- 2n 2. Guiven pokler Servies E an Here ana aan 20 Now 2n+2 (Replece in by nth in an] 2 On12 (2n+2) Now ant2 a 2042 lim ein anti 200 g no 22n 2017 an - lin. 2012 X (29+2) xen no (312) - lim no 90 | 2+an) an aan 22 x2 lim nyo (1+) (1+2) 22 I to anti Here I lim no an = 12 By Ratio test Given seories as convergent when x2 <1

-> <ar< Thore for Radius of convergence REI and Interval of convergence is re 1-1,4) Anower Now 4 8 202 ars ato + xon 아 + + fa6 Σ 10 4 8 6 27 2 ne01 - 2 1x 11-12-1 Anu mwer F(x)