0
$\begingroup$

If we let consider a simple sum such as the following:

$$\sum_{x=1}^{n}{x}=\frac{n(n+1)}{2}$$

Would it be correct to name the function that equals $\sum\limits_{x=1}^{n}{x}$ for a given upper bound, $g(n)$ or $g(x)$? I ask because the sum is written in terms of $x$ yet evaluated for inputs of $n$.

$\endgroup$
3
  • 4
    $\begingroup$ You should use $g(n)$ since the entire quantity depends only on $n$. Here $x$ is only a dummy variable inside the summation (similar to the dummy variable in integration). $\endgroup$
    – angryavian
    Commented Jan 15, 2019 at 0:54
  • 4
    $\begingroup$ On the left hand side $x$ is a bound variable while $n$ is an open variable, so the left hand side is a function of $n$ but not of $x$ $\endgroup$
    – Henry
    Commented Jan 15, 2019 at 0:55
  • $\begingroup$ x is unimportant. You could replace the occurrences of x with y or with k and it would not change the value of the sum. $\endgroup$
    – William Elliot
    Commented Jan 15, 2019 at 4:05

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .