1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/2021055
问题描述:
1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/2021055
答
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-...