1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...1/(1+2+3+...20)怎么算,
问题描述:
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...1/(1+2+3+...20)怎么算,
答
1+2+3+...+n=(1+n)*n/2.1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...1/(1+2+3+...20)=1+1/[2(2+1)/2]+1/[3(3+1)/2]+1/[4(4+1)/2]+...+1/[20(20+1)/2]=1+2/(2*3)+2/(3*4)+2/(4*5)+...+2/(20*21)=1+2[1/(2*3)+1/(3*4)...