 
|
Page 1 of 1
|
[ 3 posts ] |
|
Share: 
|
| Author |
Message |
Concyclicboy
Posts: 27
Location: República Independiente de Antiguo Cuscatlan
|
Posted: Oct 07, 2009, 3:45 pm •
# 1
Let  be the product of all non-zero digits of the positive integer  . For example,  ,  ,  ,  .
Find the value of the sum: P(1) + P(2) + ... + P(2008) + P(2009). |
|
|
pco
Posts: 3863
Location: Paris (France)
|
Posted: Oct 08, 2009, 1:41 am •
# 2
Concyclicboy wrote: Let be the product of all non-zero digits of the positive integer . For example, , , , . Find the value of the sum: P(1) + P(2) + ... + P(2008) + P(2009). 
For any  : 
So 
For any : 
So 
So   
Hence the result : 
_________________
Patrick
|
|
|
mathgeniuse^ln(x)
Posts: 5047
Location: Michigan, Born in Montreal
|
Posted: Oct 08, 2009, 8:33 pm •
# 3
Notice that the sum is essentially the same as
2(1+1+2+3+4+5+6+7+8+9)^3+2(1+1+2+3+4+5+6+7+8+9)-1=194763.
The first one can be treated as a place holder for 0.
_________________
I suck at Math
|
|
|
Share:
Moderators: MithsApprentice, N.T.TUAN, Peter, darij grinberg, orl, pbornsztein, Megus, harazi, Arne, mathmanman, High School Olympiad Moderators
|
|
Page 1 of 1
|
[ 3 posts ] |
|
