计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50

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计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
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计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50

计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/48*19-1/49*50)÷2
=(1/1*2-1/49*50)÷2
=(1/2-1/2450)÷2
=1/4-1/4900
=1224/4900
=306/1225