sumas harmónicas impares

Sum[ 1/n^{3} ] = pi^{3}·f(3)·( 1/(2^{2}+1) )·( 1/(2^{1}+(-1)) ) = ( pi^{3}/20 )

f(3) = (1/4) & 4 = 1·1·(6+(-2))

Sum[ 1/n^{5} ] = pi^{5}·f(5)·( 1/(2^{3}+1) )·( 1/(2^{2}+(-3)) ) = ( pi^{5}/288 )

f(5) = (1/32) & 32 = 2·2·(10+(-2))

Sum[ 1/n^{7} ] = pi^{7}·f(7)·( 1/(2^{3}+3) )·( 1/(2^{2}+(-1)) ) = ( pi^{7}/2970 )

f(7) = (1/90) & 90 = 3·3·(14+(-4))

Sum[ 1/n^{9} ] = pi^{9}·f(9)·( 1/(2^{4}+1) )·( 1/(2^{3}+(-7)) ) = ( pi^{9}/29750 )

f(9) = (1/1750) & 1750 = 5·5·5·(18+(-4))

... (pi^{10}/93555) < (pi^{9}/29750) < ... 

... (pi^{8}/9450) < (pi^{7}/2970) < ...

... (pi^{6}/945) < (pi^{5}/288) < ...

... (pi^{4}/90) < (pi^{3}/20) < ...

... (pi^{2}/6)