List of Common Maclaurin Series

1/(1-x) = the sum over n from 0 to infinity of x^n = 1 + x + x^2 + x^3 + ... for x in (-1,1)

exp(x) = the sum over n from 0 to infinity of (x^n)/(n!) = 1 + x + (x^2)/2 + (x^3)/6 + ... for all x

sin(x) = the sum over n from 0 to infinity of (-1)^n * (x^(2n+1))/((2n+1)!) = x - (x^3)/6 + (x^5)/120 - (x^7)/5040 + ... for all x

cos(x) = the sum over n from 0 to infinity of (-1)^n * (x^(2n))/((2n)!) = 1 - (x^2)/2 + (x^4)/24 - (x^6)/720 + ... for all x

arctan(x) = the sum over n from 0 to infinity of (-1)^n * (x^(2n+1))/(2n+1) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ... for x in [-1,1]

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