Naming a sum such as $sumlimits_{x=1}^{n}{x}=frac{n(n+1)}{2}$
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 $sumlimits_{x=1}^{n}{x}$ 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 $n$.
algebra-precalculus summation notation
edited Jan 15 at 5:42
mrtaurho
6,19771641
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
$endgroup$
add a comment |
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 $sumlimits_{x=1}^{n}{x}$ 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 $n$.
algebra-precalculus summation notation
edited Jan 15 at 5:42
mrtaurho
6,19771641
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
$endgroup$
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
Jan 15 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
Jan 15 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
Jan 15 at 4:05
add a comment |
0
0
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 $sumlimits_{x=1}^{n}{x}$ 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 $n$.
algebra-precalculus summation notation
edited Jan 15 at 5:42
mrtaurho
6,19771641
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
$endgroup$
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 $sumlimits_{x=1}^{n}{x}$ 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 $n$.
algebra-precalculus summation notation
algebra-precalculus summation notation
edited Jan 15 at 5:42
mrtaurho
6,19771641
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
edited Jan 15 at 5:42
mrtaurho
6,19771641
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
edited Jan 15 at 5:42
mrtaurho
6,19771641
edited Jan 15 at 5:42
mrtaurho
6,19771641
edited Jan 15 at 5:42
mrtaurho
6,19771641
6,19771641
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
asked Jan 15 at 0:50
GnumbertesterGnumbertester
7321114
7321114
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
Jan 15 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
Jan 15 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
Jan 15 at 4:05
add a comment |
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
Jan 15 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
Jan 15 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
Jan 15 at 4:05
4
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
Jan 15 at 0:54
$begingroup$
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
Jan 15 at 0:54
4
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
Jan 15 at 0:55
$begingroup$
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
Jan 15 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
Jan 15 at 4:05
$begingroup$
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
Jan 15 at 4:05
add a comment |
0
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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
Jan 15 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
Jan 15 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
Jan 15 at 4:05