Suppose that a power series 00 8(x) = bn x" %3D n=0 00 has the radius of convergence p > 0 , all b, are positive, and that > diverges to ∞. Then show that f(x)/g(x) converges to a as x → p- for any ,bnp" power series f(x) = L anx" %D n=0 such that a,/b, converges to a as n → ∞,

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