Sequences and series.....


by Cheman
Tags: sequences, series
Cheman
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#1
Nov7-04, 02:22 PM
P: 236
My text book says that a progression is another name for a series, but the dictionary says it is another name for a sequence - which is it?
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kreil
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#2
Nov7-04, 02:57 PM
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progression:
3. A continuous series; a sequence.
-The American HeritageŽ Dictionary of the English Language

I think it is both.
Gokul43201
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#3
Nov7-04, 03:42 PM
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A sequence is an ordered set of terms, {[itex]t_i[/itex]}
A series is a sum of terms, [itex]\sum t_i[/itex]

Mathworld defines a 'progression' as synonymous with 'sequence'.

PS : An English dictionary does not necessarily know the mathematical difference between a sequence and a series.

synergy
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#4
Nov9-04, 10:45 AM
P: 62
Cool

Sequences and series.....


A series is a special kind of sequence.

if your sequence is x1, x2, x3, x4, x5...

then the series it produces is x1, x1+x2, x1+x2+x3, x1+x2+x3+x4, ...

which we can re-label as y1, y2, y3, y4, ...

and this is a new sequence.

so if a progression is a series, then it is automatically a type of sequence.

Also, there are arithmetic progressions, geometric progressions, and others. My idea of progression is any sequence, including the special sequence called a series.
Aaron


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