SEAMO 2027 - Paper E - SET 05 - Self-study Question 12

For $r=1,2,3,\ldots$, let $u_r=1+2+\cdots+r$. Find the value of $\displaystyle\frac1{1/u_1}+\frac2{1/u_1+1/u_2}+\frac3{1/u_1+1/u_2+1/u_3}+\cdots+\frac{100}{1/u_1+1/u_2+\cdots+1/u_{100}}$.