$\sqrt {1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt {1+\frac{1}{2^2}+\frac{1}{3^2}}+\cdots+\sqrt {1+\frac{1}{2024^2}+\frac{1}{2025^2}}$

If the sum of this series can be written as $a+$ $\frac{b}{c}$ then $a+b+c=?$