1/1*1/2*1/3+1/2*1/3*1/4+1 - 知识问答

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

1个回答

1/1*2*3=1/2(1/1*2-1/2*3)
1/2*3*4=1/2(1/2*3-1/3*4)
……
1/48*49*50=1/2(1/48*49-1/49*50)
1/（1*2*3）+1/（2*3*4）+1/（3*4*5）+...+1/（48*49*50）
=1/2 (1/1*2-1/2*3)+1/2(1/2*3-1/3*4)+.+1/2 (1/48*49-1/49*502)
=1/2(1/1*2-1/2*3+1/2*3-.-1/49*50)
=1/2*(1/2-1/2450)
=612/2450
=356/1225

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