1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+9)(a+10)=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)+...+1/(a+5)-1/(a+10)=1/a-1/(a+10)=10/a(a+10)
