funció zeta 3s

∑ ( 1/k^{3(2s+1)} ) = (1/2)·( 1/( (2^{2s}+1)^{2s+1}·( 2^{2s+1}+(-1) )·( 2^{2s+2}+1 ) ) )·pi^{3(2s+1)}


∑ ( 1/k^{3} ) = ( 1/(2·2^{1}·5) )·pi^{3} = (1/20)·pi^{3}
∑ ( 1/k^{9} ) = ( 1/(2·5^{3}·7·17) )·pi^{9} = (1/29750)·pi^{9}


(1/20)·pi^{3} < (1/6)·pi^{2}
pi < (20/6) = 3.3...


(1/90)·pi^{4} < (1/20)·pi^{3}
pi < (90/20) = 4.5


(1/29750)·pi^{9} < (1/9450)·pi^{8}
pi < (29750/9450) = 3.1481...


(1/93555)·pi^{10} < (1/29750)·pi^{9}
pi < (93555/29750) = 3.1447058824