计算: 1/1*2+1/2*3+1/3*4············1/2009*2010 注:* 号代表乘号!

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计算:1/1*2+1/2*3+1/3*4············1/2009*2010注:*号代表乘号!计算:1/1*2+1/2*3+1/3*4············1/2009*2010注:*号代

计算: 1/1*2+1/2*3+1/3*4············1/2009*2010 注:* 号代表乘号!
计算: 1/1*2+1/2*3+1/3*4············1/2009*2010 注:* 号代表乘号!

计算: 1/1*2+1/2*3+1/3*4············1/2009*2010 注:* 号代表乘号!
1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
.
1/2009*2010=1/2009-1/2010
所以 1/1*2+1/2*3+1/3*4············1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+.+1/2009-1/2010
=1-1/2010
=2009/2010

=1-1/2010

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2009*2010)=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010=1-1/2010=2009/2010