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
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
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)