Let $a_n=\frac{n}{n+2}$. Find the smallest number $M$ such that:

(a) $|a_n-1|\le 0.001$ for $n\ge M$

$M=$

(b) $|a_n-1|\le 0.00001$ for $n\ge M$

$M=$

(c) Now use the limit definition to prove that $\displaystyle\lim_{n\to\infty}a_n=1$. That is, find the smallest value of $M$ (in terms of $t$) such that $\left|a_n-1\right|<t$ for all $n>M$.
(Note that we are using $t$ instead of $\epsilon$ in the definition in order to allow you to enter your answer more easily).
$M=$ (Enter your answer as a function of $t$)