谁能告诉我求1/2+1/6+1/12+1/20+……+1/420

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谁能告诉我求1/2+1/6+1/12+1/20+……+1/420
谁能告诉我求1/2+1/6+1/12+1/20+……+1/420

谁能告诉我求1/2+1/6+1/12+1/20+……+1/420
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

1/2=1-1/2
1/6=1/2-1/3
...
1/2+1/6+1/12+1/20+……+1/420=-1/21

找规律
1/2+1/6+1/12+1/20+……+1/420
=1/2+1/(2*3)+1/(3*4)+1/(4*5)+......+1/(20*21)
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/20-1/21)
=1/2+1/2-1/21
=1-1/21
=20/21

1/2+1/6+1/12+1/20+……+1/420
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+......+1/(20*21)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/20-1/21
=1-1/21
=20/21

等于1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......1/20-1/21
=1-1/21
=20/21

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