# A long limit

Calculus Level 5

The value of the limit

$$L=\displaystyle\lim_{y \rightarrow \infty} \sqrt[7]{(8y+3)(y+1)(y+2)(y+3)(2y+3)(2y+5)(4y+5)}-2y$$

is of the form $$\dfrac{A}{B}$$ where$$A$$ and $$B$$ are co-prime integers.

Find the value of $$A+B$$.

$$\textbf{Note :}$$ Do $$\textbf{NOT}$$ use wolfram alpha.

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