to make sum of series including combinations ${N\choose 1}{N\choose 0}+{N \choose 2}{N\choose 1}a^2 b^{-2} + {N\choose 3}{N \choose 2}a^4 b^{-4}+{N\choose 4}{N \choose 3}a^6 b^{-6}+...$Is it possible to sum the given series assuming $N$ is very large
${N\choose 1}$- denotes combination taking $1$ out of $N$. a and b are less than $1$ and $b=1-a$