1/2+1/(23)+1/(34)+1/(45)+……+1/(20022003)=?

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1/2+1/(2*3)+1/(3*4)+1/(4*5)+……+1/(2002*2003)=?
1/2+1/(2*3)+1/(3*4)+1/(4*5)+……+1/(2002*2003)=?

1/2+1/(2*3)+1/(3*4)+1/(4*5)+……+1/(2002*2003)=?
裂项法
1/1*2=1-1/2
1/2*3=1/2-1/3
.
1/2002*2003=1/2002-1/2003
原式
=1-1/2+1/2-1/3+1/3-1/4+.+1/99-1/100
=1-(1/2-1/2)-(1/3-1/3)-(1/3-1/3)-.-(1/2001-1/2001)-1/2002
=1-0-0-0-.-0-1/2003
=2002/2003

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