Calculus 2: power series and function. Please help me do 1-13. Please show your work thank you.Answers are already given in the photo

In #1-10, find the interval of convergence of the power series. (-1)"x 1. (-1)"x 6.> n+1 n2 n=0 n=1 2. 2" n2x n! n=0 n=1 (a - 2)" (x - 2)" 3. 8. n2+1 nn n=0 n=1 n2rn 4. 9. 2 . 4 . 6 . ... . (2n) n=1 n=1 (3.r - 2)" 5. n 3n 10. 1 . 3 . 5 . ... . (2n - 1) n=1 n=1 In #11-13, find a power series representation for the function. 3 11. f(x) = 1 - 14 2 12. f(x) = 3 _ 1 13. f(x) = 3x2 - 1 1 Final Answers 1. (-1, 1] 6. [-1, 1] 11. \\ 3rin 2. (-00, 00) 7. (-4, 2 ) n=0 2 3. [1, 3] 8. (-00, 00) 12. 3n+120 n=0 4. (-5, 3) 9. (-00, 00) 13. 312n+1 5. [-3, 3) 10. (-00, 00) n=0