Summation inside multiplication: prod[j=1,2] (sum[k=j,3] (j - k))

[MathLearner2016]

\(\displaystyle \prod_{j=1}^{2} \bigg(\sum_{k=j}^{3} (j-k)\bigg)\)


\(\displaystyle \bigg(\sum_{k=1}^{3} (1-k)\bigg) \times \bigg(\sum_{k=2}^{3} (2-k)\bigg)\)


\(\displaystyle \bigg( (1-1) + (1-2) + (1-3) \bigg) \times \bigg( (2-2) + (2-3) \bigg)\)


\(\displaystyle \bigg( (0) + (-1) + (-2) \bigg) \times \bigg( (0) + (-1) \bigg)\)


\(\displaystyle -3 \times -1\)


\(\displaystyle 3\)


Am I doing it right?

 

[Deleted member 4993]

\(\displaystyle \prod_{j=1}^{2} \bigg(\sum_{k=j}^{3} (j-k)\bigg)\)


\(\displaystyle \bigg(\sum_{k=1}^{3} (1-k)\bigg) \times \bigg(\sum_{k=2}^{3} (2-k)\bigg)\)


\(\displaystyle \bigg( (1-1) + (1-2) + (1-3) \bigg) \times \bigg( (2-2) + (2-3) \bigg)\)


\(\displaystyle \bigg( (0) + (-1) + (-2) \bigg) \times \bigg( (0) + (-1) \bigg)\)


\(\displaystyle -3 \times -1\)


\(\displaystyle 3\)


Am I doing it right?

Correct