\(\frac{k+1}{(1+2+\cdots+k)(1+2+\cdots+(k+1))}\)

Algebra Level 2

Evaluate \[\begin{align} \frac{2}{1+2} &+ \frac{3}{(1+2)(1+2+3)} \\ &+ \frac{4}{(1+2+3)(1+2+3+4)}+ \cdots \\ &+ \frac{10}{(1+2+\cdots+9)(1+2+\cdots+10)}. \end{align}\]

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