- #1

Easty

- 19

- 0

## Homework Statement

Using mathematical induction, prove the inequality

(1+a)^n >= 1+na for all a>-1 and all n

## Homework Equations

## The Attempt at a Solution

Base case

1+a >= 1+a. the inequality holds.

I am struggling with the inductive step.

by working backward, i multiply both sides by (1+a) and this gives me

(1+a)^(k+1) >= (1+ka)(1+a)

all i can think of at this point is that 1+a >= 0, but i don't think this helps me.

working the other way, starting with n=k+1, i find

(1+a)(1+a)^k>= (1+ka)+a

would is be enough to state that (1+a)> a and thus the inequality holds?

thanks in advance