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Power Series

Expand (1-z)^-m in powers of z for m in N. Let (1-z)^-m=sum from n=0 to infinity of (a_nz^n) then

a_n ~n^m-1/(m-1)! as n-> oo where ~ means that the quotient of the expressions to the left and the right of it tends to 1.

Solution Summary

Power series are investigated. The solution is detailed and well presented.