Let $X$ be the subspace of $\mathbb R^3$ which is union of the spheres of radius $1/n$ and centered at $(1/n,0,0)$. Then $X$ is simply connected.
I had thought for it in this way to attach $2$-cells to a single point, namely the origin, but then I realized the space I will get is a wedge sum of spheres and not the space given in the question.
Please help to figure out the fundamental group of the space in question.
Not a homework problem