Melody

Now Alan, I want to look at yours :)

This first one is very obvious, thank you          

$$\prod_{n=2}^K(2n-1)$$

or as:

Now this I don't  get.  

$$\frac{2^{K+1}\Gamma(K+\frac{1}{2})}{2\sqrt{\pi}}
=\frac{2^k(K-\frac{1}{2})!}{\sqrt{\pi}}\;\;?$$                  Where did $$\sqrt{\pi}$$      appear from?

where Γ() is the Gamma function

$$\Gamma (t)=\int_0^{\infty}x^{t-1}e^{-x}dx$$

It doesn't really matter, I  think this is all be above me.            

Thanks Bertie,   

You know I was really proud of myself getting that far on my own. 

I chewed on it for ages!

I have repeated your work here because I was having problems with it but by the time I had written it all out in LaTex I finally understood,  but I decided just to leave the LaTex here.   

-------------------------------------

So the number of ways that 2k people can be paired off is:

$$3*5*7*9*.....*(2k-1)\\\\
=3*5*7*9*.....*(2k-3)*(2k-1)\\\\
=\frac{1*2*3*4*.....*(2k-3)(2k-2)(2k-1)}{2*4*6*8*...(2k-2)}\\\\
=\frac{1*2*3*4*.....*(2k-3)(2k-2)(2k-1)}{2^{k-1}[1*2*3*4*...(k-1)]}\\\\
=\frac{(2k-1)!}{2^{k-1}(k-1)!}$$

THIS IS GREAT!     

I JUST HAD A THOUGHT.

Can this be extended to seperating into other groups Like 3N separated into groups of 3? 

A project for the future perhaps. 

You can't - there is no equal sign.  :)

That  is a great answer Geno.  I had forgotten that that is how it is done.  

Use atan( )

Colin did it 

colin is the cluts.  !!!

If deloris broke it 2 people are telling the truth

same if eddie broke it

same if andy broke it.

same for brenda

Colin broke it and deloris is the only truthful one 

The school that dave goes to has 180 pupils in year 9 how many pupils are there in year 7 and 8 if year 7 is 110 degrees and year 8 is 130 degrees on a pie chart.

ok lets think about this.

there is 360 degrees in a circle

yr7   is  110 degrees

yr 8  is   130 degrees

that makes  240 degrees for 7 and 8 combined

360-240=120       so year 9 is 120 degrees out of a total of 360 degrees

let x be the entire school population

(120/360)  of x = 180 students

(1/3)x=180

x=180*3 = 540 students

yr 7 is       110/360 * 540 = 165 students

and you can figure out year 8 on your own.  do it just like i did year 7     

does the shool only have years 7 8 and 9?

@@ End of Day Wrap   Sat 4/4/15    Sydney, Australia    Time 12:01am  (Really sun morn)   ♪ ♫

Good evening,

Great answers to day were given by CPhill, Alan, Civonamzuk, Rosala, Geno3141, Dogeminer and Nauseated.  Thank you.    

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