- #1

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1/2 , 1/3 , 2/3 , 1/4 , 2/4 , 3/4 , 1/5 ,2/5 ,3/5 ,4/5 ...

i cant see the patterns here?

i cant see the patterns here?

- Thread starter transgalactic
- Start date

- #1

- 1,395

- 0

1/2 , 1/3 , 2/3 , 1/4 , 2/4 , 3/4 , 1/5 ,2/5 ,3/5 ,4/5 ...

i cant see the patterns here?

i cant see the patterns here?

- #2

- 179

- 0

For the pattern, first look at the denominators only, and then look at how the numerators change for each denominator.

- #3

- 1,395

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ok i see numbers

1/2 2/3 3/4

a1 a3 a6

but they dont have constant gap between then

so i cant do a formula for that

1/2 2/3 3/4

a1 a3 a6

but they dont have constant gap between then

so i cant do a formula for that

Last edited:

- #4

- 5

- 0

That should get you started ;)

- #5

- 1,395

- 0

i see that too but i need to break into sUb sequences

what you say doesnt help me with that

what you say doesnt help me with that

- #6

- 5

- 0

- #7

- 1,395

- 0

ok i need at least two

and their location n(k) formula

and their location n(k) formula

- #8

- 179

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To describe the sequence 1, 3, 6, 10, 15, ...,ok i see numbers

1/2 2/3 3/4

a1 a3 a6

but they dont have constant gap between then

so i cant do a formula for that

n(1) = 1

n(2) = n(1) + 2

n(3) = n(2) + 3

...

n(k) = ?

If you are familiar with Pascal's triangle, you can get a "nicer" expression from it.

- #9

- 1,395

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this is a recursion

i need linear n(k) formula

i need linear n(k) formula

- #10

- 148

- 0

edit:

Take the numbers with numerator 1. They clearly form the sub-sequence 1/(k+1) k=1...∞

Now, these occur at:

1/2 -> position 1

1/3 -> position 2

1/4 -> position 4

1/5 -> position 7

1/6 -> position 11

1/n -> position ??

Hint: the distance between positions increases by one every time

Double hint: ½n² + ½n + 1

Take the numbers with numerator 1. They clearly form the sub-sequence 1/(k+1) k=1...∞

Now, these occur at:

1/2 -> position 1

1/3 -> position 2

1/4 -> position 4

1/5 -> position 7

1/6 -> position 11

1/n -> position ??

Hint: the distance between positions increases by one every time

Double hint: ½n² + ½n + 1

Last edited:

- #11

HallsofIvy

Science Advisor

Homework Helper

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One thing I see is 1/2, 2/3, 3/4, 4/5, ... which clearly converges1/2 , 1/3 , 2/3 , 1/4 , 2/4 , 3/4 , 1/5 ,2/5 ,3/5 ,4/5 ...

i cant see the patterns here?

Another is 1/3, 1/4, 1/5, ... which also converges.

As has been pointed out there are an infinite number of subsequences in any sequence. Perhaps a better question would be, "What are the subsequential limits?"

- #12

- 1,395

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so there may be endless number of limits

unless this series converges

in which case all of the sub sequences limits equal

the limit of the sequence

what to do in this case:

1/2 , 1/3 , 2/3 , 1/4 , 2/4 , 3/4 , 1/5 ,2/5 ,3/5 ,4/5 ...

??

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