Summation with two sequences

Algebra Level 5

Let an=2nn(n+2)a_n=\dfrac{2^n}{n(n+2)} and bn=3n5n+18b_n=\dfrac{3^n}{5n+18}. Find the value of n=1anbn\large\displaystyle\sum_{n=1}^{\infty}\dfrac{a_n}{b_n}

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