计算1/3×5+1/5×7+1/7×9+..

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计算1/3×5+1/5×7+1/7×9+...+1/47×49。

参考答案:

1/3×5+1/5×7+1/7×9+...+1/47×49=(1/3-1/5+1/5-1/7+1/7-1/9+...+1/47-1/49)×12=(1/3-1/49)×1/2=23/147