1/1x3+1/3x5+1/5x7+.1/49x51的简便方法

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1/1x3+1/3x5+1/5x7+.1/49x51的简便方法1/1x3+1/3x5+1/5x7+.1/49x51的简便方法1/1x3+1/3x5+1/5x7+.1/49x51的简便方法1/1x3+1

1/1x3+1/3x5+1/5x7+.1/49x51的简便方法
1/1x3+1/3x5+1/5x7+.1/49x51的简便方法

1/1x3+1/3x5+1/5x7+.1/49x51的简便方法
1/1x3+1/3x5+1/5x7+.1/49x51
=1/2 ×[2/(1x3)+2/(3x5)+2/(5x7)+.2/(49x51)]
=1/2×[(1-1/3)+(1/3-1/5)+(1/5-1/7)+.+(1/49-1/51)]
=1/2×（1-1/51)
=25/51