1\1x3+1\3x5+1\5x7+1\7x9+.+1\99x101=

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1\1x3+1\3x5+1\5x7+1\7x9+.+1\99x101=1\1x3+1\3x5+1\5x7+1\7x9+.+1\99x101=1\1x3+1\3x5+1\5x7+1\7x9+.+1\99

1\1x3+1\3x5+1\5x7+1\7x9+.+1\99x101=
1\1x3+1\3x5+1\5x7+1\7x9+.+1\99x101=

1\1x3+1\3x5+1\5x7+1\7x9+.+1\99x101=
1/2(1-1/3+1/3-1/5****+1/99-1/101)
=1/2(1-1/101)
=50/101