Can someone help me complete this easy proof by induction

Question

$P(n): for -1<x => (1+x)^n >= (1+nx)$

$P(1): (1+x) >= (1+x)$

$P(n+1): (1+x)^{(n+1)} = (1+x)^n*(1+x) ....$ where to go from here?

Answer 1

$$\text {Suppose it is valid for n, then you can multiply by }\ (1+x)\text{ both sides and get:}$$ $$\ (1+x)^n(1+x)≥(1+nx)(1+x)$$ $$\ (1+x)^{(n+1)}≥1+x+nx+nx^2≥1+x+nx=(1+(n+1)x)$$ $$\text {where the last inequality comes from the fact that }\ nx^2≥0\text{ } \forall x∈\Bbb R \text { and n }∈\Bbb N $$