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Suppose I have following series -

$1, 2, 4, 7, 11, 16, \dots$

How can I mathematically represent this series? I can't represent it as AP as d is not constant. I couldn't represent it as GP either.

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    You might want to be careful about the difference between series and sequences. A sequence is an ordered list of objects and a series is the sum of terms of a sequence. That is, you might want to make clear whether you are talking about a closed form for the sum of the first $n$ terms (the sum is obviously not convergent) or a closed form for term $n$.2012-12-18

2 Answers 2

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$n$-th term $=1 + \frac{n(n-1)}{2}$

Method of difference.

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    Check out http://www.purplemath.com/modules/nextnumb.htm , where they work out 2, 5, 10, 17, 26,....2012-12-18
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$1+0=1$

$1+1=2$

$2+2=4$

$4+3=7$

$7+4=11$

$11+5=16$

$16+6=22$

$22+7=29$

$29+8=37$

$37+9=46$

$46+10=56$

...............

...............

...............

............... Do you see the pattern now?

Can you see how you can write this as a recurrence?

See Method of Differences.

Regards -A

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    I am not sure the OP got it, was trying to guide them so they could solve it themselves. Thanks!2013-05-12