# 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 co prime integers).

$$Find$$ $$A+B$$

×