@ Tricky 'puzzle' problem from CPhill - Can YOU work it out?

 Excellent answer Heureka!

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

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

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

$$0.07958923760058268712601067554654 < 1/10$$

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!

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!!