Proof to show that sums of vectors spanning a vector space also span a vector space

Question

Let vectors $v_1, v_2, and v_3$ span a vector space $V$. Show that the vectors $v_1, v_1 + v_2$ and $v_1+ v_2 + v_3$ also span $V$.

How would I go about proving this? I understand that I have to show that the vectors are a linear combination of each other to get V; however I'm terrible at proofs and don't know how to actually write this out mathematically.

Answer 1

$$v_2=(v_1+v_2)-v_1$$ $$v_3=(v_1+v_2+v_3)-(v_1+v_2)$$