# Prove by induction that ∣z1+z2+⋯+zn∣≤∣z1∣+∣z2∣+⋯+∣zn∣ for all n∈ℕ n N . [duplicate]

• $|(z_1+\cdots+z_{n-1})+z_n|\le |z_1+\cdots+z_{n-1}|+|z_n|$ now do the same to $|z_1+\cdots+z_{n-1}|$ – user160738 Nov 18 '16 at 18:41