1/5+1/45+1/117+.+1/9797=

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1/5+1/45+1/117+.+1/9797=
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1/5+1/45+1/117+.+1/9797=
1/5+1/45+1/117+.+1/9797=

1/5+1/45+1/117+.+1/9797=
1/5+1/45+1/117+.+1/9797
=1/1×5+1/5×9+1/9×13+.+1/97×101
=1/4 (1-1/5+1/5-1/9+.+1/97-1/101)
=1/4×(1-1/101)
=1/4×100/101
=25/101

原式=1/(1*5)+1/(5*9)+1/(9*13)+……+1/(97*101)
=(1/4)*(1-1/5+1/5-1/9+1/9-1/13……+1/97-1/101)
=(1/4)*(1-1/101)
=25/101