IMSO 2023 Mathematics — International Short Answer Question 18

Let a and b be positive integers such that $\frac{1}{1\times9}+\frac{2}{9\times25}+\frac{3}{25\times49}+\cdots+\frac{15}{841\times961}=\frac ab$. If $\gcd(a,b)=1$, what is the sum of a and b?