I need a help about the following: Maple gave that the following equality is true for n =1,2,3,4,5, $$ \sum_{h=0}^{\infty}\binom{n+h}{n}{_3}F_2\left( \substack{-h,n+1,n+1\\ 1,1}; x\right)= \frac{1}{x^{n+1}}.$$

Note that ${_3}F_2\left( \substack{-h,n+1,n+1\\ 1,1}; x\right)$ is a polynomial of degree $h$.

I would like to know why that is true?
Maple fails to compute for $n=6$ in my computer, but is it true for all integer $n \geq 6$?

Where can i find such series involving hypergeometric term?