Let <a_n > be a sequence such that a_1+a_2+…+a_n=(n^2+3 n)/((n+1)(n+2)). If 28 Σ_k=1^10 1/a_k=p_1 p_2 p_3 … p_m, where p_1, p_2, …, p_m are the first…

Let $\displaystyle <a_{\mathrm{n}}>$ be a sequence such that $\displaystyle a_1+a_2+\ldots+a_n=\frac{n^2+3 n}{(n+1)(n+2)}$. If $\displaystyle 28 \sum_{k=1}^{10} \frac{1}{a_k}=p_1 p_2 p_3 \ldots p_m$, where $\displaystyle \mathrm{p}_1, \mathrm{p}_2, \ldots, \mathrm{p}_{\mathrm{m}}$ are the first m prime numbers, then m is equal to