[jacks]

Evaluation of  the sum \( \displaystyle \frac{\sum^{r}_{k=0}\binom{n}{2k}\cdot \binom{n-2k}{r-k}}{\sum^{n}_{k=r}\binom{n}{k}\cdot \binom{2k}{2r}(0.75)^{n-k}\cdot (0.5)^{2k-2r}}\ \ ,\ \ (n\geq 2r) \)

[jacks]

In answer hint as

Coefficient of \[ x^n \] in \[ (1+x+x^2)^n \]

And answer given is 1

I did not understand how they find it.