To solve the expression [tex]\(2 \left( \frac{1}{2n} \right) - 1 \left( \frac{1}{n} \right)\)[/tex] with [tex]\(n = 6\)[/tex], we will break it down into smaller steps and solve each part.
1. First, substitute [tex]\(n = 6\)[/tex] into the expression:
[tex]\[
2 \left( \frac{1}{2 \cdot 6} \right) - 1 \left( \frac{1}{6} \right)
\][/tex]
2. Calculate the first term:
[tex]\[
2 \left( \frac{1}{12} \right)
\][/tex]
Simplify it:
[tex]\[
2 \cdot \frac{1}{12} = \frac{2}{12} = \frac{1}{6}
\][/tex]
3. Calculate the second term:
[tex]\[
-1 \left( \frac{1}{6} \right)
\][/tex]
Simplify it:
[tex]\[
-1 \cdot \frac{1}{6} = -\frac{1}{6}
\][/tex]
4. Add the two terms together:
[tex]\[
\frac{1}{6} + \left( -\frac{1}{6} \right)
\][/tex]
Simplify it:
[tex]\[
\frac{1}{6} - \frac{1}{6} = 0
\][/tex]
Thus, the solution to the expression [tex]\(2 \left( \frac{1}{2n} \right) - 1 \left( \frac{1}{n} \right)\)[/tex] with [tex]\(n = 6\)[/tex] is [tex]\(0\)[/tex].
Therefore, none of the provided options [tex]\(\frac{5}{6}\)[/tex], [tex]\(\frac{11}{12}\)[/tex], [tex]\(1 \frac{1}{6}\)[/tex], [tex]\(1 \frac{1}{3}\)[/tex] are correct. The correct answer should be [tex]\(0\)[/tex], which is not listed among the given choices.
