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- #1

#### kaliprasad

##### Well-known member

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

- Thread starter kaliprasad
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- Thread starter
- #1

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

- Admin
- #2

$k$ 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.$$

- Admin
- #3

You could also write:

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

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