Melody

\({8*3^n} \over 3^{n+2}-3^{n-2}\\~\\ {8*3^n} \over 3^n3^2\;-\:3^n3^{-2}\\~\\ {8*3^n} \over 3^n(3^2\;-\:3^{-2})\\~\\ \frac{8}{3^2\;-\:3^{-2}}\\~\\ 8 \div(9-\frac{1}{9})\\~\\ 8 \div(\frac{81}{9}-\frac{1}{9})\\~\\ 8 \div(\frac{80}{9})\\~\\ 8 \times(\frac{9}{80})\\~\\ 0.9\)

Hi Juriemagic, 

Just multiply top and bottom (both) by      4+3i

That will get rid of the complex number on the bottom, then just collect like terms etc.

If you need more explanation then let us know

Thanks Rom :)

Thanks very much Rom  

It is not really answered there Heureka, we did not really understand the question...  I didn't anyway and neither did Chris.

I sort of answered but not properly.

If someone with more understanding would lke to answer can you please do it on the original question - Heureka has posted the link.

But if you do answer there, write a simple note here as well to tell us that you have added to the original post   

Prove:

\(1-8sin^2\theta cos^2\theta=cos(4\theta)\\ LHS=1-2(2sin\theta cos\theta)^2\\ LHS=1-2sin^2(2\theta)\\ LHS=1-sin^2(2\theta)-sin^2(2\theta)\\ LHS=cos^2(2\theta)-sin^2(2\theta)\\ LHS=cos(4\theta)\\ LHS=RHS \qquad\\ QED \)

Yes I accept that   

How many 3-digit numbers between 100 and 999 are there with the property that each digit, from the left, beginning with the 2nd is > than the digit before it, and the 3rd is > than the 2nd, such as : 123, 234, 456....etc? And how many more 6-digit such numbers are there between 100,000 and 999,999? Any help would be great. Thank you. 

It stands to reason that 0 cannot be one of the digits and all the digits must be different. 

How many ways can 3 digits be chosen from 9, that would be 9C3=84

For each of those triples there is only one way that they can be placed in ascending order

So the answer is 84

You can now work out the number of 6 digit combinations for yourself.  It will be done in the same way.

Thanks for your answers Anthrax and Ben.  

But...

Ben, it would have sounded an aweful lot nicer if you had started with something like:

'Antrax, I do not think your answer is right because .......'

If you had actually asked the question, which you didn't, then I'd also suggest that you started with 'Thanks'

Opening with

'You are wrong', 

or   'Your result is incorrect' 

or similar statements is a great way to get our esteemed answerers off side, and there is nothing acheived by doing that.