There is a previous question regarding a decreasing Sigma Notation Sequence (Decreasing Sigma Notation Sequence), however I feel this question is sufficiently different. I am wondering why you could not write the summation of the sequence of {10, 9, 8, ..., 2, 1} as $\sum_{j=10-k+1}^{10} {j}$?
For example,
when k=1, $\sum_{j=10-1+1}^{10} {j} = \sum_{j=10}^{10} {j} = 10$.
when k=2, $\sum_{j=10-2+1}^{10} {j} = \sum_{j=9}^{10} {j} = 9+10$.
when k=3, $\sum_{j=10-3+1}^{10} {j} = \sum_{j=8}^{10} {j} = 8+9+10$.