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Show that the series k = 0 ( 1 ) k k + 2 x k has a sum function f : ( 1 ,

Show that the series

k=0(1)kk+2xk

has a sum functionf:(1,1)R given by

f(x)=x21(xlog(1+x)),x=0

and f(0) = 1/2.

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