Summing Conditional Products

Calculus Level 5

\[\lim_{n \to \infty} \dfrac{\displaystyle\sum abcde}{n^{10}}=\dfrac{A}{B}\]

subject to the condition that \(1 \leq a \leq b \leq c \leq d \leq e \leq n\). Find \(A+B\).

\(\textbf{Note :} \ A,B\) are co-prime integers. The answer is exact, not an approximation.

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