find the taylor series of the given function ,please if i compare the origin fun

Mathematics
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please i need if i compare the origin with this function  ,what we did for both side (steps)

for example  the origin is 1/1-z =sum 0-infinity of  z^n   |z|<1

   what we do for both side to get the given function  ,then what the final tayolr series

Dec 13th, 2014

f(z) = 1/(1-z)                                  f(o) =1

f’(z) =-1/(1-z)2(-1)                         f’(0) =1

f”(z) = (1)(-2)/(1-z)3(-1)                 f’’(0) =2!

f n (z) = (1)(2)…(n) /(1-z)n+1          fn(0) = n!

f(z)   =   f(0) +z f’(0)/1!+z2f’’(0)/2!+ …zn fn(0)/n!+..

  =  1+z+z2 2!/2!+z33!/3!+…zn n!/n!+…

  =   1+z+z2+z3+………zn+…


Dec 13th, 2014

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Dec 13th, 2014
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