Hello.

I got stuck on this:

Show using the binomial theorem, that if $\displaystyle a>1$ then $\displaystyle \lim_{n\rightarrow\infty}a^n=+\infty$

Hereīs my brave attempt:

$\displaystyle (1+(a-1))^n=\sum_{k=1}^{n}\binom{n}{k}1^{n-k}(a-1)^k$

$\displaystyle =\binom{n}{1}(a-1)+\binom{n}{2}(a-1)^2+...+\binom{n}{n}(a-1)^n$

So at first I thougt that each term is bigger than one (this is the part that I got wrong). Then, since there are n terms, the sum must tend to infinity because n tends to infinity and since each term bigger than one.

The b part:

Show that

$\displaystyle \lim_{n\rightarrow\infty}n^{-1}a^n=+\infty$

I want to try this myself after getting the a) part straight but I wonder is there a clue in the b part for solving a?

Any hints, besides replacing my toilet paper with my home assignment?