MACLAURIN 'S SERIES

STANDARD SERIES

Exponential Series :

f(x)     = e^x =>    f(0)   = e^0 = 1
f '(x)   = e^x =>   f''(0)   = e^0 = 1
f ''(x)   = e^x =>   f ''(0) = e^0 = 1
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f (n)(x) = e^x =>   f(n)(0) = e^0 =1

Hence,  

 e^x  = 1+ x + (x^2)/2! + (x^3)/3! +...+(x^n)/n! ....     for all value of x.

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