+0  
 
+1
366
11
avatar+713 

One day, River writes down the numbers 1,2,3,...999

 

What is the sum of all the digits that River wrote down?

 

thanks and please help :)

 May 3, 2020
 #1
avatar+171 
0

Using the formula \(\frac{1}{2}(n)(n+1)\), we substitute the \(n\) as \(999\) to get \(\boxed{499500}\).

 May 3, 2020
 #3
avatar+713 
0

sorry, but it says it's wrong... thanks for helping though :)

lokiisnotdead  May 3, 2020
edited by lokiisnotdead  May 3, 2020
 #2
avatar+26011 
0

This is an arithemtic series with d = 1

 

S = (n/2) Γ— (2a + (nβˆ’1)d)

S = sum = 999/2 (2 + 998(1))

               = 499500  

 May 3, 2020
 #5
avatar+713 
0

sorry, that's wrong too... thanks for taking the time to help though :)

lokiisnotdead  May 3, 2020
 #4
avatar+713 
0

Just to clarify: the problem asks the sum of all the digits that he wrote down. 

 May 3, 2020
 #6
avatar
+1

189 , 300 , 300 , 300 , 300 , 300 , 300 , 300 , 300 , 300 >>Total = 2889

 May 3, 2020
 #8
avatar+713 
+1

thanks Guest! even though this isn't the answer, your explanation was the part I was stuck on! (I couldn't figure out how many 1s, 2s, 3s, etc. there were) 

 

So the answer is 1+2+3...9 =45 *300 = 13500.\(\)

lokiisnotdead  May 3, 2020
 #9
avatar
+1

Sorry, I did have both of them but didn't read the question correctly:

 

(189, 300, 300, 300, 300, 300, 300, 300, 300, 300) >>>Total Number = 2889
(0, 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700)>>Total Sum = 13500

Guest May 3, 2020
 #10
avatar+713 
0

great job Guest! 

 

thanks for helping!!! I really appreciate it :)))

lokiisnotdead  May 3, 2020
 #7
avatar
0

Each digit is written 99 times, so the sum is (0 + 1 + 2 + ... + 9)*99 = 4455.

 May 3, 2020
 #11
avatar+131 
+1

This is an AoPs question from counting and probability...

 

STOP POSTING AOPS QUESTIONS HERE

 May 4, 2020

17 Online Users

avatar
avatar