MathDB
E 23

Source:

May 25, 2007
inductionnumber theoryprime numbers

Problem Statement

Let p1=2,p2=3,p3=5,⋯ ,pnp_{1}=2, p_{2}={3}, p_{3}=5, \cdots, p_{n} be the first nn prime numbers, where n≥3n \ge 3. Prove that 1p12+1p22+⋯+1pn2+1p1p2⋯pn<12.\frac{1}{{p_{1}}^{2}}+\frac{1}{{p_{2}}^{2}}+\cdots+\frac{1}{{p_{n}}^{2}}+\frac{1}{p_{1}p_{2}\cdots p_{n}}< \frac{1}{2}.
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