求1x2,2x3,3x4,4x5,……98x99,99x100的倒数和如题

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求1x2,2x3,3x4,4x5,……98x99,99x100的倒数和如题

求1x2,2x3,3x4,4x5,……98x99,99x100的倒数和如题
求1x2,2x3,3x4,4x5,……98x99,99x100的倒数和
如题

求1x2,2x3,3x4,4x5,……98x99,99x100的倒数和如题
原式=1-1/2+1/2-1/3+···+1/99-1/100
=1-1/100
=99/100

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/(99*100)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/98-1/99)+(1/99-1/100)
=1-1/100
=99/100

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