If graph G has 2n+1 vertices where every vertex has degree at least n, G is connected So I need to show that each pair of vertices is joined by a path, or show that there is a vertex joined to every other vertex by a path.

But.. how?
Let $u,v$ be any two vertices. If they aren't connected directly, then $u$ has at least $n$ neighbours and $v$ has at least $n$ neighbours. If all mentioned vertices were distinct, we would get $2n+2$ vertices. Can you conclude from here?
Let $e$ be the number of edges in $G$.Use Handshaking theorem $\sum_1^{2n+1}deg(v)=2e$

$\rightarrow[n(2n+1)/2]\le{e}$..............................................$(1)$

Use the fact that a graph with $n$ vertices that contains more than $(n-1)(n-2)/2$ edges is connected.Replacing $n$ by $2n+1$ in this, we see that $(1)$ holds true, hence $G$ is connected.