一道初一数学题！！很难做啊

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+1/2009-1/2010
=1-1/2010
=2009/2010
1/1*3+1/3*5+1/5*7+……+1/2007*2009
=1/2*(1-1/3+1/3-1/5+1/5-1/7+..-...-1/2007+1/2007-1/2009)
=1/2*(1-1/2009)
=1004/2009
1/1*4+1/4*7+1/7*10+……+1/2008*2011
=1/3*(1-1/4+1/4-1/7+1/7-1/10+..-...-1/2008+1/2008-1/2011)
=1/3*(1-1/2011)
=2008/6033
1/n*(n+k)
=1+k/n

1/1*2+1/2*3+1/3*4+……+1/2009*2010=2009/2010
1/1*3+1/3*5+1/5*7+……+1/2007*2009=1004/2009
1/1*4+1/4*7+1/7*10+……+1/2008*2011=670/2011
1/n*(n+k)=(1/n-1/(n+k))/k

我上初一时咋就没有这样的题啊

应该挺难的