My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 8th, 2018, 08:46 AM   #1
Newbie
 
Joined: Sep 2018
From: US

Posts: 1
Thanks: 0

Sum of a non-decreasing sequence of integers

For which pairs of positive integers $(n, d)$ is it true that every integer $S$ can be written as a sum of a non-decreasing sequence of integers $a_1+a_2+...+a_n$ and $a_n-a_1=d$?
Jimbob81345 is offline  
 
September 8th, 2018, 03:09 PM   #2
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,129
Thanks: 914

That's sure confusing, Jimbo.
Are you talking about an arithmetic sequence?

Say sequence is 1,2,3
a1=1, a2=2, an = 3 (n = 3)
1 + 2 + 3 = 6 = S ?
(n,d) = 3,2)?

What does "every integer S" mean? Any integer?
Denis is offline  
September 8th, 2018, 05:56 PM   #3
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,403
Thanks: 2477

Math Focus: Mainly analysis and algebra
I have a vague feeling that there may be no such pairs.

I have a stronger feeling that I'm probably wrong about that.
v8archie is offline  
September 8th, 2018, 06:06 PM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,129
Thanks: 914

Quote:
Originally Posted by v8archie View Post
I have a vague feeling that there may be no such pairs.

I have a stronger feeling that I'm probably wrong about that.
I have a still stronger feeling that you're drunk
Denis is offline  
September 8th, 2018, 07:09 PM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,403
Thanks: 2477

Math Focus: Mainly analysis and algebra
Nothing stronger than tea tonight. (Sorry Jonah, you can have mine).
v8archie is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
integers, nondecreasing, sequence, sum



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Prove that X contains a strictly decreasing sequence? NeoXx Real Analysis 3 November 23rd, 2015 02:39 PM
sequence increasing or decreasing aaron-math Calculus 4 November 6th, 2011 09:26 AM
Sequence of integers proglote Number Theory 5 October 19th, 2011 10:37 AM
Sequence of integers proglote Number Theory 4 October 11th, 2011 07:11 AM
Sequence (eventually) increasing or decreasing or neither everettjsj2 Calculus 2 February 25th, 2010 08:26 PM





Copyright © 2018 My Math Forum. All rights reserved.