Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is Tn(x) = x + 1 2

Chapter 8, Problem 61

(choose chapter or problem)

Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is Tn(x) = x + 1 2 x3 3 + 1 3 2 4 x5 5 ++ 1 3 5 (n 2) 2 4 6 (n 1) xn n

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