1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?

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1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?
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1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?
1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?

1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?
1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99*100)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/98-1/99+1/99-1/100
=1-1/100
=99/100