Answer:
yes
Step-by-step explanation:
The associative and commutative properties of multiplication allow you to rearrange the product to the form shown in the question.
Division by 2 is effectively multiplication by 1/2.
![(n\times(n+1))/2\qquad\text{given}\\\\=\dfrac{n(n+1)}{2}=\dfrac{n}{2}(n+1)\\\\=\boxed{(n/2)(n+1)}](https://tex.z-dn.net/?f=%28n%5Ctimes%28n%2B1%29%29%2F2%5Cqquad%5Ctext%7Bgiven%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bn%28n%2B1%29%7D%7B2%7D%3D%5Cdfrac%7Bn%7D%7B2%7D%28n%2B1%29%5C%5C%5C%5C%3D%5Cboxed%7B%28n%2F2%29%28n%2B1%29%7D)
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<em>Additional comment</em>
Evaluation of the expressions according to the <em>order of operations</em> will proceed differently for the two expressions.
For the first expression, evaluation steps are ...
- add 1 to n
- multiply the sum by n
- divide the product by 2
For the second expression, evaluation steps are ...
- divide n by 2
- add 1 to n
- multiply the results of these two operations
As we said above, the properties of multiplication ensure the results are the same either way.
As a practical matter, for integer values of n, one of n and (n+1) will be even. It is usually convenient to divide the even number by 2. This means the evaluation might be ...
- ((n+1)/2)n . . . . for odd n
- (n+1)(n/2) . . . . for even n
For certain computer representations of the numbers, results may differ depending on the specific numbers and the order of evaluation.