到底谁能够告诉我原版 谁能够告诉我1/2+1/6+1/12+1/20+1/30+……+1/9900=?

谁能够告诉我1/2+1/6+1/12+1/20+1/30+……+1/9900=?  

谁能够告诉我1/2+1/6+1/12+1/20+1/30+……+1/9900=?

=1-1/2+1/2-1/3+……+1/99-1/00
=1-1/100
=99/100

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

1/6+1/12+1/20+1/30+.+1/9900=?

原式=(1/2-1/3)+(1/3-1/4)+......(1/99-1/100)
=1/2-1/100
=49/100

1/6+1/12+1/20+1/30+.+1/9900

(1/2-1/3)+(1/3-1/4)+(1/4-1/5)...............+(1/99-1/100)
=1/2-1/100
=49/100

1/6+1/12+1/20+1/30+······+1/2007*2008＝多少

1/(2*3)+1/(3*4)++······+1/(2007*2008)=1/2-1/3+1/3-1/4+^+1/2007-1/2008=1/2-1/2008=1003/2008

1/6+1/12+1/20+1/30+···+1/2005X2006=？

1/6+1/12+1/20+1/30+···+1/2005X2006
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(2005X2006)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+...+(1/2005-1/2006)
=1/2-1/2006
=501/1003

1/6+1/12+1/20+1/30+···+1/2009*2010（完整的 嘻）

1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+……+1/(2009*2010)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+……+(1/2009-1/2010)
=1/2-1/2010
=1004/2010
=502/1005

1/6+1/12+1/20+1/30+．．．+1/72

1/6+1/12+1/20+1/30+．．．+1/72
=1/2*3+1/3*4+1/4*5+1/5*6+...+1/8*9
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/8-1/9
=1/2-1/9
=7/18

1/2+1/6+1/12+1/20+……+1/9900等于多少？急！

(1-1/2)+(1/2-1/3)+.....+(1/99-1/100)=1-1/100=99/100

1/6+1/12+1/20+1/30+.+1/2009*2010=？

1/6+1/12+1/20+1/30+........+1/2009*2010
=1/(2*3)+1/(3*4)+1/(4*5)+......+1/(2009*2010)
=(1/2-1/3)+(1/3-1/4)+........+(1/2009-1/2010)
后面的就不用说了吧。