MHB To write summation decreasing index

[kaliprasad]

how to write a summation with decreasing index

say for adding from index 1 to n for $x_k$ we write $\sum^{n}_{k=1}x_k$.

how do we write the above for index to go from n to 1 down wards

 

[I like Serena]

Mathematically they are identical, aren't they?
$k$ really iterates over a set of elements, which is unordered.
So there wouldn't be a separate mathematical notation for it.

Improvising, we might write:
$$\sum^{1}_{k=n}x_k$$
or:
$$\sum_{k=n,...,1}x_k$$
or:
$$\left|\begin{array}{}
s \leftarrow 0 \\
\text{for }k\leftarrow n \text{ downto } 1 \\
\quad s \leftarrow s + x_k \\
s
\end{array}\right.$$

 

[MarkFL]

You could also write:

$$\sum_{k=1}^n x_{n-k+1}$$