This is my code:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{textcomp}
\usepackage{dsfont}
\usepackage{graphicx}
\usepackage[english]{babel}
\usepackage{hhline}
\usepackage{fancyvrb}
\begin{Verbatim}[fontsize=\large]
$${r \choose r} + {r+1 \choose r} + {r+1 \choose r} + ..... + {n
\choose r} = {n+1 \choose r+1} $$
\end{Verbatim}
we will prove this by using induction on n. \\
$$\sum_{n=1}^{\infty} 2^{-n} = 1$$
as you can see in the picture it's not being displayed for some reason. Can someone help?
N.B: the stuff i wrote is far from done so don't judge me on that one :D

\\before a math display. – David Carlisle Dec 03 '17 at 17:34\\at the end of any paragraph (including the partial paragraph before a display) you will get a spurious "white " line of the paragraph which stops the display adapting to the real last line of the paragraph and will give bad line and page breaking behaviour. – David Carlisle Dec 03 '17 at 18:08