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Math Help - What is the Infinite series (sum) of a constant?

  1. #1
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    What is the Infinite series (sum) of a constant?

    I have the following sums: SUM[from 0 to 0] of 1; SUM[from 0 to 1] of 1; SUM[from 0 to 3] of 1.
    What are these sums and why. No elaborate proof is necessary, but I would like to know what's going on here. Thanks
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  2. #2
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    Quote Originally Posted by afried01 View Post
    I have the following sums: SUM[from 0 to 0] of 1; SUM[from 0 to 1] of 1; SUM[from 0 to 3] of 1.
    What are these sums and why. No elaborate proof is necessary, but I would like to know what's going on here. Thanks
    The sum is just the number of terms in the sum (since the value of each term is 1 we are just counting how many 1's we are adding, so the first sum is 1, the second 2, ..)

    CB
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    reply to first answer

    Thank you
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    Note that none of those are infinite series.

    \displaytype\sum_{i= 0}^n a_i= a_0+ a_1+ \cdot\cdot\cdot+ a_n. An infinite sum of any non-zero constant does not converge.

    In particular, \displaytype\sum_{i= 0}^0 1= 1 (that is for i= 0; one term)
    \displaytype\sum_{i= 0}^1 1= 1+ 1= 2 (that is for i= 0 and 1; two terms)
    \displaytype\sum_{i= 0}^2 1= 1+ 1+ 1= 3 (that is for i= 0, 1, and 3; three terms)
    and
    \displaytype\sum_{i= 0}^3 1= 1+ 1+ 1+ 1= 4 (that is for i= 0, 1, 2, and 3; four terms)
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    reply to second answer

    Thanks!
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