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单词 arithmetic series
释义
arithmetic series

Physics
  • A series or progression of numbers in which there is a common difference between terms, e.g. 3, 9, 15, 21,… is an arithmetic series with a common difference of 6. The general formula for the nth term is

    [a+(n-1)d]

    and the sum of n terms is

    n[2a+(n-1)d]/2.

    Compare geometric series.


Mathematics
  • A series a1 + a2 + a3 + … (which may be finite or infinite) in which the terms form an arithmetic sequence. Let sn be the nth partial sum (that is, the sum of the first n terms). Then sn is given by the formula sn=12n(a+l) where a is the first term and l is the last (nth) term. In particular, when a = 1 and the common difference d = 1:

    r=1nr=1+2++n=12n(n+1).


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