# What is $$\sum _{r=1}^n r^7$$?

Calculus Level 4

Let $$\displaystyle M_n= \sum_{r=1}^n r^4 , N_n= \sum_{r=1}^n r^2$$ and $$\displaystyle Y_n= \sum_{r=1}^n r^7$$. If $$\displaystyle \lim_{n\to\infty} \dfrac{M_n N_n}{Y_n}$$ can be expressed as $$\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers.

Find $$A+B$$.

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