# Thread: Induction question help needed

1. ## Induction question help needed

Prove by induction that

(1 +x)**n ≥ 1 + nx

i have never seen a induction question set up like this before ... could i get some assistance please

im confused as to how to use both n and x in the question

2. ## Re: Induction question help needed

You are using a notation that is not standard for many mathematicians. This was already mentioned in response to one of your previous posts. Standard notation to indicate an exponent is ^, not **. Your posts will be easier for the general community to read if you try to learn LaTeX (and use  or $\$\ tags) or use notation that is more familiar to most mathematicians.

For your question, I assume that $\displaystyle x$ can be any real number, and $\displaystyle n$ is a positive integer. Start with the base of induction:

$\displaystyle (1+x)^1 = 1+x = 1+1x$

Note: if $\displaystyle n=0$, then it is still true for all $\displaystyle x\neq -1$, as $\displaystyle (1+x)^0=1=1+0x$ for all $\displaystyle x\neq -1$.

Assume it is true for all positive integers up to some value $\displaystyle n$. Then try to show that $\displaystyle (1+x)^{n+1} \ge 1+(n+1)x$. Hint: $\displaystyle (1+x)^{n+1} = (1+x)(1+x)^n$.

3. ## Re: Induction question help needed

yeah i realize that i a problem ill research how to do that ... thanks for the help ill look at it and try to continue