+0  
 
0
35
1
avatar

Find the largest positive integer n such that 1/1000 + 2/2000 + 3/1000 + ... + n/1000 < 1.

 May 11, 2020
 #1
avatar+1543 
+1

So 2/2000 = 1/1000.

 

so we have 1+1 + 3 + 4 + ... n /1000 < 1

 

So 2 + 3 + ... n < 1000

 

1 + 2 + 3... 50 = 51 * 25 = 1275, -1, 1274

 

1 + 2 + 3... 40 = 41 * 20 = 820, -1, 819

 

We have 1 + 2 + 3... 44 = 45 * 22 = 990, -1, 989

 

We can't go more. 

 

Thus n = 44

 

On the case that you messed up and it's 2/1000, it's still the same answer, but this time, added is 990.

 

If you don't understand anything feel free to ask.

 May 11, 2020

17 Online Users