Hello,
I think I went wrong somewhere here.
Particularly in the last 2 lines.
Here is a pic of my attempt:
https://www.dropbox.com/s/zkdwts5uhzfuwdy/ex1.1_q47.jpg
Hello,
I think I went wrong somewhere here.
Particularly in the last 2 lines.
Here is a pic of my attempt:
https://www.dropbox.com/s/zkdwts5uhzfuwdy/ex1.1_q47.jpg
Not a useless question, just hard to read.
We have a LaTeX system on site. Check out the LaTeX help forum.
-Dan
Verify that for n>=1 $\displaystyle 1 + \frac{\1}{1!} + \frac{\1}{2!} + \frac{\1}{3!}+ ... + \frac{\1}{n!} \leq 3 - \frac{\1}{n}$
My attempt:
1. Proved for n
2. Assumed for k:
$\displaystyle 1 + \frac{\1}{1!} + \frac{\1}{2!} + \frac{\1}{3!}+ ... + \frac{\1}{k!} \leq 3 - \frac{\1}{k}$
3. prove for k+1
$\displaystyle 1 + \frac{\1}{1!} + \frac{\1}{2!} + \frac{\1}{3!}+ ... + \frac{\1}{k!} + \frac{\1}{k+1!}\leq 3 - \frac{\1}{k+1}$
$\displaystyle \leq 3 - \frac{\1}{k}+ \frac{\1}{k+1!}$
$\displaystyle \leq 3 - \frac{\1}{k}+ \frac{\1}{k+1 * k!}$
$\displaystyle \leq 3 - \frac{\1}{k}+ [ \frac{\1}{k+1} * [3- \frac{\1}{k}]]$
factoring out 3 - 1/k
never mind i figured out my mistake, i didn't realize to leave a 1 when factoring something from itself.
Thanks,