1=2/2
1/(1+2) = 2/2×3 =2(1/2-1/3)
1/(1+2+3 ) = 2/3×4 =2(1/3-1/4)
1/(1+2+3+4 ) = 2/4×5 =2(1/4-1/5)
........
1/(1+2+3+ ... + n) = 2/n(n+1)=2(1/n - 1/(n+1)
1+1/(1+2)+1/(1+2+3)+....+1/(1+2+3+...+n)=4024/2013
2 ×[1/2+1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + .... + 1/n - 1/( n +1)]=4024/2013
2 × [ 1 - 1/(n +1) ] =4024/2013
1 - 1/(n +1) = 2012/2013
(n + 1 - 1 )/(n+1)= 2012/2013
n × 2013 = 2012(n +1)
2013n = 2012n + 2012
2013n - 2012n = 2012
n = 2012
