series tests

Basic Maclaurin Series sinx = x? x3 3! + x5 5! ? x7 7! + ? ? ? = ?? n=0 (?1)nx2n+1 (2n + 1)! ?? < x < +? cosx = 1? x2 2! + x4 4! ? x6 6! + ? ? ? = ?? n=0 (?1)nx2n (2n)! ?? < x < +? ex = 1 + x + x2 2! + x3 3! + x4 4! + ? ? ? = ?? n=0 xn n! ?? < x < +? sinhx = ex ? e?x 2 = x + x3 3! + x5 5! + x7 7! + ? ? ? = ?? n=0 x2n+1 (2n + 1)! ?? < x < +? coshx = ex + e?x 2 = 1 + x2 2! + x4 4! + x6 6! + ? ? ? = ?? n=0 x2n (2n)! ?? < x < +? 1 1? x = 1 + x + x2 + x3 + x4 + ? ? ? = ?? n=0 xn ?1 < x < 1 ln(1 + x) = x? x2 2 + x3 3 ? x4 4 + ? ? ? = ?? n=1 (?1)n+1xn n ?1 < x ? 1 arctanx = x? x3 3 + x5 5 ? x7 7 + ? ? ? = ?? n=0 (?1)nx2n+1 2n + 1 ?1 ? x ? 1 (1 + x)k = 1 + kx + k(k ? 1)x2 2! + k(k ? 1)(k ? 2)x3 3!