1+1/[1+2]+1/[1+2+3]+...+1/[1+2+3+...+10]
=1+2[1/2-1/3]+2[1/3-1/4]+...+2[1/10-1/11]
=1+2[1/2-1/3+1/3-1/4+...+1/10-1/11]
=1+2[1/2-1/11]
=1+1-2/11
=20/11