r=2
#..................................................................
#..................SAGE.CODE.USED.TO.BUILD.........................
#.......................THE.TABLE..................................
#.................OF PARTIAL SUMS FOR ZETA.........................
#..................................................................
#.....................PLEASE.FEEL.FREE.............................
#.....................TO.SEND.COMMENTS.............................
#..................................................................
#..............Sage.is.a.free.open-source..........................
#..............mathematics.software.system.........................
#................licensed.under.the.GPL............................
#...............http://www.sagemath.org/...........................
#..................................................................
S=lambda n: sum(1/k^r for k in range(1,n+1))
Z=[S(10^i).n(digits=5) for i in range(7)]
#............................
Nom_fichier='Zeta_partiel'+str(r)+'.html'
o=open(Nom_fichier,'w')
o.write('<table border="1" >')
o.write('\n')
o.write('<tr>')
o.write('\n')
o.write('<td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></td><td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S(n)</mi></math></td>')
o.write('\n')
o.write('</tr>')
o.write('\n')
for i in range(7):
   o.write('<tr>')
   o.write('\n')
   o.write('<td>'+str(10^i)+'</td><td>'+str(Z[i])+'</td>')
   o.write('\n')
   o.write('</tr>')
o.write('\n')
o.write('</table>')
o.close()