Find the following limit

The limit can be written as $\displaystyle\lim_{n \to \infty}\dfrac{1}{n}\sum_{k=1}^{n} \left(\dfrac{k}{n}\right)^{p}$ , which is in the form of a Riemann sum with $x = \dfrac{k}{n}$ , and thus is equivalent to

$\displaystyle\int_{0}^{1} x^{p} dx = \left(\dfrac{x^{p+1}}{p + 1}\right)_{0}^{1} = \dfrac{1}{p + 1}$ . With $p = 106$ , we then have $\dfrac{A}{B} = \dfrac{1}{107} \Longrightarrow A + B = \boxed{108}$ .