Bài giải:

$(1-\frac{1}{3})\times (1-\frac{1}{6})\times (1-\frac{1}{10})\times (1-\frac{1}{15})\times ....\times (1-\frac{1}{780})$

= $\frac{2}{3}\times \frac{5}{6}\times \frac{9}{10}\times ....\times \frac{779}{780}$

= $\frac{4}{6}\times \frac{10}{12}\times \frac{18}{20}\times ....\times \frac{1558}{1560}$
= $\frac{4\times 10\times 18\times ...\times 1558}{6\times 12\times 20\times ...\times 1560}$

= $\frac{(1\times 4)\times \left( 2\times 5 \right)\times (3\times 6)\times ...\times \left( 37\times 40 \right)\times \left( 38\times 41 \right)}{\left( 2\times 3 \right)\times (3\times 4)\times (4\times 5)\times ...\times (39\times 40)}$
Giản ước ta còn
$\frac{41}{3\times 39}=\frac{41}{117}$
Ta được:
$\frac{41}{117}$ x A = 1
A = 1 : $\frac{41}{117}$
A = 117/41