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summation (Topic)
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"summation" is owned by drini. [ full author list (7) | owner history (1) ]
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See Also: Einstein summation convention, series, addition, plus sign

Other names:  sum, summing, sigma notation, $\sum$
Also defines:  running
Keywords:  sum, sigma, notation, evaluating, progression, sequence
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Cross-references: Fibonacci number, series, absolute value, chess, quotient, odd, arithmetic, difference, sequence, arithmetic progression, arithmetic progressions, similar, consecutive, Gauss, calculate, product, obvious, range, reduced, constant term, factor, associativity, commutativity, properties, prime numbers, reciprocals, specifications, infinite, upper limit, parameter, variations, complex numbers, roots of unity, terms, even, algebraic structure, lie on, function, odd numbers, even numbers, positive, representation, integers, represent, index, variable, equivalent, expression, compact
There are 624 references to this entry.

This is version 18 of summation, born on 2004-10-12, modified 2007-03-13.
Object id is 6361, canonical name is Summation.
Accessed 77943 times total.

Classification:
AMS MSC: 00A05 (General :: General and miscellaneous specific topics :: General mathematics)
 11B25 (Number theory :: Sequences and sets :: Arithmetic progressions)
Pending Errata and Addenda
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checking accuracy: first example with infinity by Tooniner on 2007-03-13 11:12:05
While I'm no mathematician, I remain an interested observer. It seems to me that the example given above for summation of 1/2^k for k=1 to infinity is incorrect.

It is given as 1/1+1/2+1/4+1/8+... but should be 1/2+1/4+1/8+... since the series starts at k=1 and 1/2^1 = 1/2.

If the series had started at k=0, then 1/2^0 would give us 1/1 and thus the series that was printed (1/1+1/2+1/4+...) would have been correct.

Am I correct or did I miss something in analytic geometry?

[ reply | up ]
Hi all old mathematicians (corrected) by pahio on 2004-10-12 19:16:09

Which is the value of the sum

 SIGMA_{i = 1}^4 of 2i+1,

is it 21 or 24? I have always (in 44 years) seen only such a practice, that the summing operator, similarly as the deriving and integral operators, affects only the first term (or addend) on its right side. This implies e.g. that SIGMA x + SIGMA y does not mean double summing
SIGMA (a + SIGMA b).
[ reply | up ]
Hi all old mathematicians by pahio on 2004-10-12 19:09:36

Which is the value of the sum

 SIGMA_{i = 1}^4 of 2k+1,

is it 21 or 24? I have always (in 44 years) seen only such a practice, that the summing operator, similarly as the deriving and integral operators, affects only the first term (or addend) on its right side. This implies e.g. that SIGMA x + SIGMA y does not mean double summing
SIGMA (a + SIGMA b).
[ reply | up ]
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