Last 1000 digits puzzle

What are the last $1000$ digits of

$$1 + 50 + 50^2 + \dots + 50^{999}$$

when written in base-$10$?

i.e.

What are the last $1000$ digits of

$$\sum_{k=0}^{999} 50^k$$

Of course, the idea is to find a way to find this manually/mathematically, and only use a calculator/computer if needed.

You don't have to list the $1000$ digits, just some simple, reasonably easy to compute (by a human) description would do too.

[Solution]