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fraction sequences

lboogy
in Analysis and Calculus

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Hi everyone,

 

I have to do some coursework, and I am studying independant of school - so I have no tutor. I am doing some coursework on sequences of fractions. I'm just wondering, after finding the formula for the nth number, what else can you do with sequences?

 

Here is what I have to do:

 

1/1 1/2 1/3 1/4 1/5 1/6 ... ...

 

the difference from above is

 

1/2 1/6 1/12 1/20 1/30 ... ...

 

the difference from above is

 

1/3 1/12 ... ... ...

 

'invesigate further'

 

I'm not sure how to investigate further! I can find the formula, but then what? How can I investigate this further?

I naturally don´t know how to interpret your coursework, either. So just a few suggestions what one could investigate about sequences:

- What is the value of the n´th number (e.g. the 10051th)? What is the value of the n'th difference between numbers (e.g. the 6252th)?

- Is there a biggest and/or a smallest number in the series? If so, which? Otherwise, why not?

- Is there a "greater than" or "lesser than" relation between subsequent numbers?

  • Author

so how would i find the formula to calculated the nth number when the sequences are fractions?

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