# Log problem.

• November 28th 2011, 01:17 PM
BabyMilo
Log problem.
$\frac{1}{n}-\frac{-1^n}{n^2}<0.000001$

can i solve this algebraically?
if not, how do i solve it?

many thanks. (Nod)
• November 28th 2011, 02:45 PM
Amer
Re: Log problem.
$\frac{n - (-1)^n}{n^2} < \frac{1}{1000000}$

take n even 2k instead of n

$\frac{2k - 1}{4k^2} < \frac{1}{1000000}$

can you solve it ??

try n odd sub 2k+1 instead of n
• November 29th 2011, 11:23 AM
BabyMilo
Re: Log problem.
for even, k>499999
for odd, k>500000

how to i proceed?

i can see if i add the two ks, it comes to k>1000001

is this the way to do it?

many thanks. :)
• November 29th 2011, 11:29 AM
Quacky
Re: Log problem.
for even, $k>499999$ So $\frac{n}{2}>499999$ remembering that $n=2k$

for odd, $k>500000$ So $\frac{n-1}{2}>500000$ remembering that $n=2k+1$

What is the solution which satisfies for all $n$?