## Question

###### Writr clearly thanks! 1. Determine the radius and interval of convergence of the following power series....

writr clearly thanks!

1. Determine the radius and interval of convergence of the following power series. Name all tests used for full credit (2x-4) k Radius: Interval: 2. Given S(x)=Ë (-1)*** find S"(x). Write answer using summation notation. 4*k!

## Answers

By Ratio Test of convergence E 2x-4)* K=1 L = Lim akti LI Ko ak Lim (k) K+ (22*4) K+ (2xth) ko Lim ko (2x+4) 1+1 K (2x4) for Radius of convergence. 22 1 +4 x +5 2 Henie 1) 2 Interval Radius (R) of Convergence of Convergence Lim art! LI K00 ak K+ k lim 21 (2x-4) (k+1) (2x-4) koo 2x -4 Video LI (1+1) 126-41 2) -IL 27-4 LU -| 2*an 2x 24+) 4-1 L2x ras CZ 2 classeHence 3 are 25 Now, 2=3 in original equation: for equality plug (2x-4) k Š (243)--) 츠 K kal K k=1 K к *راد) is shall conusse by peseries fesnele. with altsnating series. K ha tok? Similarly for x=s ap not I (268 (213)-4) * ) shell onverge. As it kas k ka will diverse bo Interval could be 로스가는 S 2 2 코도 2 Interval Niwl NIG

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