The Riemann zeta function is the subject of extensive research and is associated with several renowned unsolved problems. It is defined byWhen x is a real number, the zeta function becomes a p-series. For even positive integers p, the value ofis known exactly. For example,

Use the estimation techniques described in the text to approximate (whose values are not known exactly) with a remainder less than 10^-3.

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3(x) = k* х k=1 Ś(p)