Prime Numbers Inequality | prime zeta function at 2

 
Prime Zeta Function
http://mathworld.wolfram.com/PrimeZetaFunction.html

Prime zeta function at 2
http://oeis.org/A085548

0.4522474200410654985065… = 1/2^2 + 1/3^2 + 1/5^2 + 1/7^2 + 1/11^2 + 1/13^2 + …

 
Can you prove that

1/2^2   +   1/3^2   +   1/5^2   +   1/7^2   + … +   1/(2*3*5*7* …)   <   1/2

That is, the sum of reciprocal of squares of all prime numbers plus the inverse product of all primes is less than   1/2

 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Math Beauty, Number Puzzles and tagged . Bookmark the permalink.

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