Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts
31 July 2011
30 July 2011
Day 1 problem
How many zero are the end of 
Solution
The formula of permutation is 
. Then 
so we'll find zero the end of 10000! and 9987!.
there are![n_{1}=\left [\frac{10000}{5} \right ]=2000](http://data.artofproblemsolving.com/images/latex/4/4/5/445a043215b3812d2d7bfc6b8bbb130291bae326.gif "n_{1}=\left [\frac{10000}{5} \right ]=2000")
integers less than 
which are multiples of 
,
and![n_{2}=\left [\frac{10000}{5^2} \right ]=400](http://data.artofproblemsolving.com/images/latex/5/7/0/57031668596fb5f42ece86e756cd77c5fc98985f.gif "n_{2}=\left [\frac{10000}{5^2} \right ]=400")
which are multiples of 
,
and![n_{3}=\left [\frac{10000}{5^3} \right ]=80](http://data.artofproblemsolving.com/images/latex/b/4/3/b43c17e9cac041c4b23364cbffc733f2459e6aff.gif "n_{3}=\left [\frac{10000}{5^3} \right ]=80")
which are multiples of 
,
and![n_{4}=\left [\frac{10000}{5^4} \right ]=16](http://data.artofproblemsolving.com/images/latex/b/c/3/bc3c0dcfc898dca25db0a81b309116ec13246660.gif "n_{4}=\left [\frac{10000}{5^4} \right ]=16")
which are multiples of 
,
and![n_{5}=\left [\frac{10000}{5^5} \right ]=3](http://data.artofproblemsolving.com/images/latex/8/5/3/8536ffad98253caa858446cd456a566bc544d9d8.gif "n_{5}=\left [\frac{10000}{5^5} \right ]=3")
which are multiples of 
,
so we get
zero are the end of 
By the same way we get
zero are the end of 
So there are
are the end of .
Please correct me! by leave your comment . Thanks
. Then so we'll find zero the end of 10000! and 9987!.
there are
integers less than which are multiples of ,and
which are multiples of ,and
which are multiples of ,and
which are multiples of ,and
which are multiples of ,so we get
zero are the end of By the same way we get
zero are the end of So there are
are the end of .Please correct me! by leave your comment . Thanks
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