Question

一道初中数学题，求解答，急急急

2/1*3+2/3*5+2/5*7+.......+2/2009*2011

Answer 1

一项一项的看，2/1*3=1-3/1，2/3*5=3/1-5/1........一次类推，最后写出来就是1-3/1+1/3-1/5+1/5-1/7+...+1/2009-1/2011=2010/2011，消掉互为相反数的项就好啦

Answer 2

2/1*3+2/3*5+2/5*7+...2/2009*2011
=1-1/3+1/3-1/5+1/5-1/7+……+1/2009-1/2011
=1-1/2011
=2010/2011

Answer 3

(1-1/3)+(1/3-1/5)+(1/5-1/7)+...........+(1/2009-1/2011)=1-1/2011=2010/2011

Answer 4

2/1*3+2/3*5+2/5*7+.......+2/2009*2011
=（1/1-1/3）+(1/3-1/5)+(1/5-1/7)+……+（1/2009-1/2011）
=1/1-1/3+1/3-1/5+1/5-1/7+……+1/2009-1/2011
=1-1/2011
=2010/2011
解本题的关键是发现规律：2/[n*(n-2)]=1/n-1/(n-2)

Answer 5

原式=1-1/3+1/3-1/5+1/5-1/7..........-1/2009+1/2009-1/2011
=1-1/2011=2010/2011