Identity of sum $\sum_{a}^{b}x=-\sum_{b}^{a}x$

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Does $\sum_{a}^{b}x=-\sum_{b}^{a}x $ is correct?

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No, reversed indexes are interpreted as either

  • no term in the sum (i.e. $0$) or

  • same as in the normal order.

But never opposite of the sum.