1/(5*7)+1/(7*9)+1/(9*11)+……+1/(99*101)=

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1/(5*7)+1/(7*9)+1/(9*11)+……+1/(99*101)=
1/(5*7)+1/(7*9)+1/(9*11)+……+1/(99*101)=

1/(5*7)+1/(7*9)+1/(9*11)+……+1/(99*101)=
1/(5*7)+1/(7*9)+1/(9*11)+……+1/(99*101)
=(1/2)*(1/5-1/7+1/7-1/9+1/9-1/11+.+1/99-1/101)
=(1/2)*(1/5-1/101)
=(1/2)*(96/505)
=48/505

1/(5*7)+1/(7*9)+1/(9*11)+……+1/(99*101)
=(1/2)*(1/5-1/7+1/7-1/9+1/9-1/11+....+1/99-1/101)
=(1/2)*(1/5-1/101)
=(1/2)*(101-5)/505
=(1/2)*(96/505)
=48/505