Induction Proof and real analysis

Question

Can someone please solve the following. I'm not good at proofs by induction. I know the base case but I don't know how to solve it after that for $(N+1)$

Let $a_1, a_2, · · · , a_n ∈ R,,$ where n is a positive integer greater than or equal to 2. Use induction to prove that $|a_1 + a_2 + · · · + a_n| ≤ |a_1| + |a_2| + · · · + |a_n|$.

Answer 1

Step $1$:

You can prove step $1$

for $n=2$

$|a_1 + a_2| ≤ |a_1| + |a_2|$.

Step $2$:

Assume that it is true for $n=k$

$|a_1 + a_2 + · · · + a_k| ≤ |a_1| + |a_2| + · · · + |a_k|$.

for $n=k+1$

$|a_1 + a_2 + · · · + a_k+a_{k+1}| ≤ |a_1 + a_2 + · · · + a_k|+|a_{k+1}| ≤ |a_1| + |a_2| + · · · + |a_k|+|a_{k+1}|$.