\(\small\mathrm{Given\ the\ infinite\ sum:} \) \(\small{S= 1+\frac{2^2+1}{2^3+1}+\frac{3^2+1}{3^3+1}+\frac{4^2+1}{4^3+1}\cdots}\)

\(\small\mathrm{What\ can\ we\ say\ about\ this\ sum?}\)

\(\small\mathrm{\mathbf{Rule}: Solve\ it\ without\ using\ the\ comparison\ test}\)

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