Question

Some numbers can be expressed as the sum of a string of consecutive positive numbers. Which numbers have this property?

Answer 1

Is there more to the question? This question doesn't seem to be very well posed. (In other words, there are plenty of assumptions we need to make before answering it.)

Answer 2

All numbers but the power of 2.

Answer 3

I should add, all POWERS of 2.

Answer 4

i stilll dont understand

Answer 5

Try it out.
9 = 2+3+4
But say 16:
4+5+6 = 15, 5+6+7=18. You can't do it.

Answer 6

@finaiized , how do you go about proving this is true? :)

Answer 7

theres some examples but i dont understand how to do it
9 = 2 + 3 + 4
11 = 5 + 6
18 = 3 + 4 + 5 + 6

Answer 8

I'm not sure if this completely counts as proof, but the reason is that powers of 2 have no even factors other than 1. And two consecutive numbers (one of which must be odd) cannot be represent a power of 2.

Answer 9

@inthemoment666 What do you mean "How to do it?" Do you not understand the example? Or the answer?

Answer 10

so pretty much has to be an even number right?

Answer 11

@inthemoment666 -- Do you know what the phrase "powers of 2" means? For example, can you name the first four "powers of 2"? This is helpful for understanding the discussion. :)

Answer 12

Not an even (look at your example: 18. It has odd factors, like 9). Only numbers that aren't Power of 2.

Answer 13

@mathteacher1729 - Powers of 2 are in the form \(2^n\). The first four (excluding n=0) is 2, 4, 8, 16, 32.

Answer 14

@finaiized I was asking @inthemoment666 , not you. :-p

Answer 15

@mathteacher1729 - Aww derp. Didn't read :P

Answer 16

okay i think i get it?

Answer 17

@finaiized You also gave the first FIVE powers of two... where I had asked for the first FOUR. :-p

Answer 18

@inthemoment666 Can you name the first five powers of THREE? :) (understanding the phrase "powers of... a number" is important.

Answer 19

yeah i know what POWER means
there 9 27 81
right?

Answer 20

Yep.

Answer 21

i feel dumb D':

Answer 22

(But @mathteacher1729 asked you for five... I just mentioned it because he burned me when I listed more than 4 :( )

Answer 23

i dont care i got it did i not

Answer 24

Yes. As to this question, I'm not sure if your teacher expects you to know this off the bat or what. But it's something you can remember I guess.

Answer 25

9 = 2 + 3 + 4
then what do i do with the problems

Answer 26

This is an interesting question in number theory which deals with divisibility. It requires lots of guessing and testing (and/or) a pretty sophisticated understanding of the factors and divisibility of numbers. Out of curiosity -- what class is this question from?

Answer 27

you want a hint? think of numbers that cannot be expressed as such a sum
also note that as in your above example
\(\frac{2+3+4}{3}=3\) i.e. \(9=3\times 3\)
also try \(4+5+6+7=22\) and \(\frac{4+5+6+7}{4}=5.5\) the number half way between 5 and 6

Answer 28

meaning of course that \(22=11\times 2\)

lets try another one
\(6+7+8+9+10=40\) and \(\frac{6+7+8+9+10}{5}=8\) so
\[40=8\times 5\]

Answer 29

so far we have
\[9=3\times 3\]
\[22=2\times 11\]
\[40=8\times 5\] keep trying and you will notice something
if you still need help let me know

Answer 30

@Numbers Hello!