Power Series Help

Question

Looking for a power series representation for tan^-1(4x^2) at a=0. This problem has really stumped me so any help would be appreciated!

Answer 1

tan^-1(x) = x - x³/3 + x⁵/5 - x⁷/7+ ...

tan^-1(4x²) = 4x² - 4³x⁶/3 + 4⁵x¹⁰/5 + ...

sum from n =0 to infinity of (-1)ⁿ(4²ⁿ⁺¹x⁴ⁿ⁺²/(2n+1)

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