Question

☺ find the ridius and interval Convergence of the following (check endpoint ह (x-3) Aal

Answer 1

(x-gin Sol: E an for the internas vergence we abblag ratio test accordin to ratio test we know Lim nxoo an here an: (-3.ph so, anti lygint so, (x-334 anti tim n400 larg yon tim 1(x-2) x n+1 lim -gr nt I (x-3) Tatt 2001 noo ap Atoo for ho

So, 1 x (x-3) | Page No. Date: we know that If Power series than conna Nerde lim ant) an So, 1x(4-3)] < -1 < x x 3) < So, ge2-3x - 120 ge2 - 3x + 170 For x2-3x + 120 XE 3-V13 2 g +113 2 x2 = 3x - 1.20 x= 3 + VT

for x2-3x +170 x = 100, 3-rs. Ju / 3tr5 a) Page No. (Date: 1 s g2-3 T+120 x-surs 50 3.813 3.5 3+VS 3 + V13 SO, xe (g-va , &- vs. Jul 13 + S 3 +113 Hence Interval of convergence 13-113 3-N 37N 3 + Nig 2 2 2 2. 2. and end points is 3 - Ng, 3.5, 35 318 radius of convergence we know that tim bn R LAAT no here bna