How to find a probability that sum of geometric variables is less than a number

Let ${X}_{i},i=1,\dots ,n$ be Geometric i.i.d random variables, which represent the number of fails, with parameter p.

Calculate or estimate from above and below:

$P(\sum _{i=1}^{n}{X}_{i}\le A),\phantom{\rule{1em}{0ex}}A\in N.$

I know that sum of the geometric random variables is the negative binomial, but I would not know all the parameters for the negative binomial r.v.

Let ${X}_{i},i=1,\dots ,n$ be Geometric i.i.d random variables, which represent the number of fails, with parameter p.

Calculate or estimate from above and below:

$P(\sum _{i=1}^{n}{X}_{i}\le A),\phantom{\rule{1em}{0ex}}A\in N.$

I know that sum of the geometric random variables is the negative binomial, but I would not know all the parameters for the negative binomial r.v.