1 + 1 + 2 of 1 + 1 + 2 + 3 of 1 + 1 + 2 + 3 + 4 of 1 + 1+2+3+…… +1 out of 100 = simple calculation, thank you for your help

1 + 1 + 2 of 1 + 1 + 2 + 3 of 1 + 1 + 2 + 3 + 4 of 1 + 1+2+3+…… +1 out of 100 = simple calculation, thank you for your help

∵1+2=2*3/2 1+2+3=3*4/2 1+2+3+4=4*5/2 1+2+3+…… +100=100*101/2 ∴1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+...+100) =1+2/(2*3)+2/(3*4)+2/(4*5)+…… +2/(100*101) =2[(1/2+1/(2*3)+1/(3*4)+...