# Thread: What is the Infinite series (sum) of a constant?

1. ## 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

2. Originally Posted by afried01
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

Thank you

4. Note that none of those are infinite series.

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

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

Thanks!

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# summation of constant from zero to constant numbet

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