1/1x3 + 1/3x5 + 1/5x7+.+.+1/99x101简便算法,

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1/1x3 + 1/3x5 + 1/5x7+.+.+1/99x101简便算法,

1/1x3 + 1/3x5 + 1/5x7+.+.+1/99x101简便算法,
1/1x3 + 1/3x5 + 1/5x7+.+.+1/99x101
简便算法,

1/1x3 + 1/3x5 + 1/5x7+.+.+1/99x101简便算法,
1/1x3 =1/2(1-1/3)
1/3x5=1/2(1/3-1/5)
.
1/99x101=1/2(1/99-1/101)
所以
原式=1/2(1-1/3+1/3-1/5+1/5-1/7.+1/99-1/101)
=1/2(1-1/101)
=1/2(100/101)
=50/101

=1/2(1-1/2+1/2-1/5+1/5-1/7.....+1/99-1/101)
=1/2(1-1/101)
=1/2*100/101
=50/101