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24
E 24
E 24
Source:
May 25, 2007
inequalities
floor function
logarithms
limit
number theory
prime numbers
Problem Statement
Let
p
n
p_{n}
p
n
again denote the
n
n
n
th prime number. Show that the infinite series
∑
n
=
1
∞
1
p
n
\sum^{\infty}_{n=1}\frac{1}{p_{n}}
n
=
1
∑
∞
p
n
1
diverges.
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