1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n（n+1）【*=乘以 /=分之】两分钟够了吧

1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n（n+1）【*=乘以 /=分之】两分钟够了吧
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*2010
1/n（n+1）【*=乘以 /=分之】
两分钟够了吧

1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*20101/n（n+1）【*=乘以 /=分之】两分钟够了吧
1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2009-1/2010
=1-1/2010
=2009/2010

1/1*2+1/2*3+1/3*4+1/4*5……+1/2009*2010
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010

=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+(5-4)/4*5……+(2010-2009)/2009*2010
=(2/1*2-1/1*2)+(3/2*3-2/2*3)+(4/3*4-3/3*4)+(5/4*5-4/4*5)……+(2010/2009*2010-2009/2009*2010)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5……+1/2009-1/2010
=1-1/2010
=2009/2010