+0  
 
+3
609
4
avatar+94083 

Hi Chris I am just reposting it here where people will see it!!

I have referenced this puzzle address in the Sticky Topic "Puzzle" thread.

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

Melody......Here's a problem that I ran into some time ago:

Show that

(1/2)*(3/4)*(5/6)*(7/8)*..............*(97/98) *(99/100) <  (1/10)

It's "tricky" ......but simple.......all at the same time.

 

Maybe some of the members  - or even, non-members - would like to try their hand at proving it !!

One word of warning.......your calculator won't do you any good on this one !!!

 

And ....as a "silly" problem...see if some of the users can figure THIS one out!!

Show that:    sinx / n  = 6

  

Melody  May 12, 2014

Best Answer 

 #2
avatar+94083 
+8

 Excellent answer Heureka!

$$\frac{1*3*5*7......*99}{2*4*6*8*......*100}\\\\
\frac{1*3*5*7......*99}{1}\times \frac{1}{2*4*6*8*....*100}\\\\
\frac{100!}{2*4*6*...*100}\times \frac{1}{2*4*6*8*....*100}\\\\
\frac{100!}{2^{50}(1*2*3*4*....*50)}\times \frac{1}{2^{50}(1*2*3*4*....*50)}\\\\
\frac{100!}{2^{50}(50!)}\times \frac{1}{2^{50}(50!)}\\\\
\frac{100!}{2^{100}\times 50!\times 50!}\\\\$$

 

$${\frac{{\mathtt{100}}{!}}{\left({{\mathtt{2}}}^{\left({\mathtt{100}}\right)}{\mathtt{\,\times\,}}{\mathtt{50}}{!}{\mathtt{\,\times\,}}{\mathtt{50}}{!}\right)}} = {\mathtt{0.079\: \!589\: \!237\: \!600\: \!582\: \!7}}$$

$$0.08<\frac{1}{10}$$

Melody  May 12, 2014
 #1
avatar+20530 
+8

 

$$0.07958923760058268712601067554654 < 1/10$$

heureka  May 12, 2014
 #2
avatar+94083 
+8
Best Answer

 Excellent answer Heureka!

$$\frac{1*3*5*7......*99}{2*4*6*8*......*100}\\\\
\frac{1*3*5*7......*99}{1}\times \frac{1}{2*4*6*8*....*100}\\\\
\frac{100!}{2*4*6*...*100}\times \frac{1}{2*4*6*8*....*100}\\\\
\frac{100!}{2^{50}(1*2*3*4*....*50)}\times \frac{1}{2^{50}(1*2*3*4*....*50)}\\\\
\frac{100!}{2^{50}(50!)}\times \frac{1}{2^{50}(50!)}\\\\
\frac{100!}{2^{100}\times 50!\times 50!}\\\\$$

 

$${\frac{{\mathtt{100}}{!}}{\left({{\mathtt{2}}}^{\left({\mathtt{100}}\right)}{\mathtt{\,\times\,}}{\mathtt{50}}{!}{\mathtt{\,\times\,}}{\mathtt{50}}{!}\right)}} = {\mathtt{0.079\: \!589\: \!237\: \!600\: \!582\: \!7}}$$

$$0.08<\frac{1}{10}$$

Melody  May 12, 2014
 #3
avatar+94083 
+3

This one still has not been answered.

 

And ....as a "silly" problem...see if some of the users can figure THIS one out!!

Show that:    sinx / n  = 6

Hint: It is not that hard!

Melody  May 12, 2014
 #4
avatar+92367 
+3

Nice answer, Heureka.......maybe I should have been more explicit....No calculators allowed!!!

(Besides, there's a simple way to "solve" this without a calculator!!)

But....I suppose I'll have to "grandfather" you into the "club," because you did provide a proof!!

CPhill  May 12, 2014

11 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.