谁能告诉我求1/2+1/6+1/12+1/20+… - 知识问答

谁能告诉我求1/2+1/6+1/12+1/20+……+1/420

5个回答

原式=1/（1*2）+1/（2*3）+1/（3*2）+1/（4*5）+……+1/（20*21）
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5-...-1/20+1/20-1/21
=1-(1/2-1/2)-(1/3-1/3)-(1/4-1/4)-...-(1/20-1/20)-1/21
=1-0-0-0-0-...-0-1/21
=1-1/21
=20/21

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