Math Is Fun Forum

Hi bob,

I am studying  modular arithmetic, diophantine equations, linear congruences, prime numbers and logic. And we are supposed to be able to prove statement concerning those topics.
for example:
prove 2^n > n^2 for all n greater than 2.

If you need more info, let me know.

Your multiplication by the conjugate is wrong from step 1 to step 2.

Yes I know but I am not sure which test would apply now...is this a geometric series? No. Can I use divergence test(n-th term test) on this? I dont think so because this is similar to the case of harmonic series combined with an alternating series(which converges even though the harmonic series diverges by itself).
With the comparision test or limit comparision test...I am not sure what to compare to, -1^n sqrt(n)?
Integral test wont work, this is not a p-series, AST, ASET, root and ratio all dont work.

Therefore by deduction LCT or Comparision Test should do it!

Thanks for pointing that out, but that still doesnt solve the problem. Fixed post #8
and my post above is still correct.

I got stuck using Alternating Series Test(aka Leibniz Test), cant do Ratio or Root Test and currently I am trying to see what happens to the partial sums of this series.

I am not sure if thats supposed to help as wolfram says ratio test is inconclusive:

http://www.wolframalpha.com/input/?i=su … D+1+to+inf

Oh!
I know of the trick just that the way you wrote it out the first time made it seems like each proceeding step is equal to the previous one.

It was a homework question on one of my assignments.

Yes it does

GCD(8,1024) = 8
GCD(2,1024) = 2
GCd(4,1024) = 4

hence 8 = 4*2

No I need help with another question and its easier to continue in this thread than create another.

Prove GCD(ab,c) = GCD(a,c) * GCD(b,c)