$$\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\dots+\frac{1}{2014\cdot2015}=\frac{m}{n},$$ where $\frac{m}{n}$ is irreducible. 
a) Find $m+n.$
b) Find the remainder of division of $(m+3)^{1444}$ to $n{}$.