[Guest]

I thought of this sequence myself and didn't find it on the forum though it might be hidden somewhere in the hundreds of posts with the word sequence in them. I also googled it and found no results so hopefully this hasn't been done before

The hard step: find the next term in the following sequence 0,2,4,6,4,2,4,6,8,6,12,2

The easy step: whats the summation of the reciprocals of every term in this sequence (from the 1st to infinith term)?

make sure to give your reasoning for what the next term is. I wont tell you if it's right if you just randomly guess it with no justification. As soon as you realize what the sequence is, you should know the summation.

[Guest]

Well the "easy step" is easy.. its infinity as you have first term 0 and the reciprocal is 1/0 (infinty)

[Guest]

Well the "easy step" is easy.. its infinity as you have first term 0 and the reciprocal is 1/0 (infinty)

lol not that easy actually. I meant to say from the second term to infinity but since i forgot to, lets go aheda and make 0 the 0th term.

[Guest]

Well the "easy step" is easy.. its infinity as you have first term 0 and the reciprocal is 1/0 (infinty)

1/0 is not infinity, its undefined.

[Guest]

1/0 is not infinity, its undefined.

[Guest]

1/0 is not infinity, its undefined.

It IS infinity.

Consider Limit for b tends to zero for a/b

As an example consider a =1 and b as 10^-x Now keep increasing x and see what a/b results.

However, 0/0 is undefined.

Agreed.

[Guest]

1/0 is not infinity, its undefined.

It IS infinity.

Consider Limit for b tends to zero for a/b

As an example consider a =1 and b as 10^-x Now keep increasing x and see what a/b results.

However, 0/0 is undefined.

[Guest]

as to whether 1/0 is infinity, i'd say no. though its true limit 1/x as x approaches 0 from the positive side, this equals infinity, but if you approach it from the negative side you get negative infinity. therefore it cannot equal any value including infinity. that is 0*infinity doesn't equal 1.

to the original problem though, i have absolutely no idea on that sequence. at first i thought it was simply going up and down, but the 12 throws a wrench in that idea. there is no clear pattern that i can see other than all the numbers being even.

[Guest]

It IS infinity.

Consider Limit for b tends to zero for a/b

As an example consider a =1 and b as 10^-x Now keep increasing x and see what a/b results.

However, 0/0 is undefined.

Er, no actually, it is undefined.

For starters, infinity is not a number, but a quantity that is greater than any real number. Secondly, for y/x = z to be defined, there must exist a unique solution for y, which is the product xz. This is not the case when x = 0, for any values of y and z. For example, if we say that 1/0 = z, then it must be true that 0*z= 1, and there is no z for which this holds true. Furthermore, the value of y could be anything, so y/0 = z (= infinity) does not have a unique solution for y.

Edit: Missing quote tags...

Edited July 16, 2009 by d3k3

[bonanova]

* Moderator Hat On *

The OP asks to evaluate the series.

Infinite or undefined, the first reciprocal is problematical.

The OP has asked us to ignore it.

Does anyone have a clue about the next term of the sequence, or about the sum?

* Moderator Hat Off *

Infinity, in this forum, seems to be self-defining:

Infinity: The number of posts that will be made on the subject before consensus is reached.

The silver lining is that posts can be assigned integer values, so it's a countable infinity.

[Guest]

(0x2)(1x2)(2x2)(3x2)(2x2)(1x2)(2x2)(3x2)(4x2)(3x2)(2x2)(1x2)(2x2)....ect. So next number would be 4. I would not be suprised if thats not correct but its all I got for now, still working on it

[Guest]

(0x2)(1x2)(2x2)(3x2)(2x2)(1x2)(2x2)(3x2)(4x2)(3x2)(2x2)(1x2)(2x2)....ect. So next number would be 4. I would not be suprised if thats not correct but its all I got for now, still working on it

Thank you for attempting the sequence instead of just discussion 1/0 lol. But sorry 12 isn't a typo. You have to be creative to solve this sequence.

nice name by the way.

[Guest]

Out of curiosity...

Is this a true sequence or just a pattern? (according to my definition...)

That is, is there one formula for all steps in the sequence, or does the formula change as the pattern increases?

Perhaps this is better asked: Is it a logical sequence or a mathematical sequence? If mathematical, does it require a knowledge of Calculus to understand, or do simple arithmetic/geometric skills function assuming sufficient cognitive skills?

Or am I asking too much??

[Guest]

let's say it's number theory (big hint). You dont need calculus to solve it's series either, just logic. If you want to call it a pattern, you can but know the "formula" for the pattern doesn't change as it goes. as i said already, you will need a little creativity to solve this.

[Guest]

wow so many views and no new guesses. maybe i should just reveal the answer.

[Guest]

The hard step: find the next term in the following sequence 0,2,4,6,4,2,4,6,8,6,12,2

How did you came up with this?

Nevermind, how about:

(0,2,4,6,4,2,4,6,8,6,12,2,10)

32 16 8 4 2 1

0 0 0 0 0 0 >> 0

0 0 0 0 1 0 >> 2

0 0 0 1 0 0 >> 4

0 0 0 1 1 0 >> 6

0 0 0 1 0 0 >> 4

0 0 0 0 1 0 >> 2

0 0 0 1 0 0 >> 4

0 0 0 1 1 0 >> 6

0 0 1 0 0 0 >> 8

0 0 0 1 1 0 >> 6

0 0 1 1 0 0 >> 12

0 0 0 0 1 0 >> 2

0 0 0 1 1 0 >> 10

Are you trying to draw a serpent on binary? lol That's my creativity working 110%!!!

Probably this is not the answer and if it is the right number I'm sure it's not the right explanation. Can you reveal the base of the series? I mean the first numbers of the series that the formula is based on? (Fibonacci is 0,1,1,x,x,x,x,x,x,x,x)

Edited July 28, 2009 by trozen2040