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# A series question: Taylor series allow us to write a f(x) in term of series.But what if given series and to solve for f(x)? For example,if I have 1+1/2+1/4+1/8+1/16+...1/2n... (n goes to infinite) then how can I combine it with 1/(1-x)?Can I solve all the power series using something like inverse Taylor series?? I can not make sure a function just by knowing f(o)=1,f(0)=1,f(0)=2...

MIT 18.01 Single Variable Calculus (OCW)