4分之1+28分之1+70分之1+...+4038088分之1
=1/3*3*[4分之1+28分之1+70分之1+...+4038088分之1]
=1/3*3*[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+...+1/2008-1/2011]
=1/3*(1-1/2011)
=1/3*2010/2011
所以一个用2010/2011个 1/3
4分之1+28分之1+70分之1+...+4038088分之1
=1/3*3*[4分之1+28分之1+70分之1+...+4038088分之1]
=1/3*3*[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+...+1/2008-1/2011]
=1/3*(1-1/2011)
=1/3*2010/2011
所以一个用2010/2011个 1/3