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In Problems 1-8, find the convergence set for the given power series. 1. IM8 (n - 1)! 2. 8 1M & iM 8 3. 6. n IM & IM 8 (x + 1)" 8. n!In Problems 9-28, find the convergence set for the given power series. Hint: First find a formula for the nth term; then use the Absolute Ratio Test. 9. X 1 .2 2.3 3-4 5.6 13. x + 2x2+ 3x3 + 4x4+ ... 15. 1 - x + 2 3 4In Problems 1-10, find the power series representation for f(x) and specify the radius of convergence. Each is somehow related to a geometric series (see Examples I and 2). 1. f(x) = 1 + x 6. f(x) = 3 + 2x 10. f(x) = tan t diIn Problems 13-16, use the result of Example 3 to find the power series in x for the given functions. 13. f(x) = e-* 14. f(x) = xetIn Problems 17-24, use the methods of Example 5 to find power series in x for each function f. 17. f (x) = ex.. 1 - X 18. f(x) = ex tan x