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    #1
    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

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    #2
    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:
    $$\left|\begin{array}{}
    s \leftarrow 0 \\
    \text{for }k\leftarrow n \text{ downto } 1 \\
    \quad s \leftarrow s + x_k \\
    s
    \end{array}\right.$$

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    #3
    You could also write:

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

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