1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/2021055
=1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+……+2010)
=2/(1*2)+2/(2*3)+2/(3*4)+2/(4*5)+……+2/(2010*2011)
=2*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2010-1/2011)
=2*(1-1/2011)
=4020/2011
1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/2021055
=1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+……+2010)
=2/(1*2)+2/(2*3)+2/(3*4)+2/(4*5)+……+2/(2010*2011)
=2*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2010-1/2011)
=2*(1-1/2011)
=4020/2011