Question

Find the interval of convergence for the series. (Enter your answer using interval notation.) 4n + 1 (-1)" +1 (5x) (2n + 1)! n = 0 (-00,00) Find the radius of convergence for the series. R = 4. [3/6 Points) DETAILS PREVIOUS ANSWERS Find the interval of convergence for the series. (Enter your answer using interval notation.) зах? n = 1 n 1 1 3'3 :) Find the radius of convergence for the series. R =

Answer 1

Criven that E (-ight inti (5x)unti (2n+1)! 20 (-1)*** (ight? Here an and Орн (2n+3)! (2n+1)! By the Ratio test - nu) (2n+ 3)! lim X n+2 lim RE a un an anh (21+1)! (-1)" 10 has a no lins (2n+3) (2n+1)! (2n+1)! = lim (2n+3) no R=es * radius of Convergence. and intervale of Convergence. I = (-00,00)

4. Criven that e zh sh nel Here 39 an theorent By Cauchy Hadamard کی۔ 3 a lim Sols - Å = lim fault neo R no =) R= 14/3 la radius of Convergence. and interval of Convergence le) < wol- =) -1/2 < x < 1 check the end points : Ź (3) Ž ħ is divergent by potest. st n=1 no Hon 39 is convergent by Lebuitz test. 6 and n na nal So, interval of Convergence ['s, 5)