# Proof by Induction:

I lost points on this proof because its incomplete and not descriptive enough. any suggestions?

If $a_i$ $\geq$ $0$, i $\geq$ 1

then, (1+$a_1$)(1+$a_2$)…..(1+$a_n$)$\geq$ 1 + $a_1$ + $a_2$ + ….. + $a_n$

Proof by Induction:

case(n=1), we have (1+$a_1$) $\geq$ 1 + $a_1$ is true.

suppose true for n $\geq$ 1.

Then (1+$a_1$)(1+$a_2$)….(1+$a_n$)(1+$a_{n+1}$) $\geq$ (1+$a_1$ + $a_2$ + …$a_n$)(1+$a_{n+1}$)

By the inductive hypothesis,

1+$a_1$+$a_2$+…..+$a_n$+$a_{n+1}$+$a_{n+1}$($a_1$+….+$a_n$) $\geq$ 1 + $a_1$ +….+$a_{n+1}$

Therefore by induction,