=1/1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+4+5+6+7+8+9)
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/(9*10)
=2*(1/1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10)
=2*(1/1-1/10)
=2*(9/10)
=9/5