how to write $X_1 X_2 + X_2 X_3$ in the form of Summation?

Question

i am trying to write this formula

$$X_1 X_2 + X_2 X_3$$

in the form of summation.

is this right?

$$\sum_{i < j} X_i X_j, \quad i,j \in\{1,2,3\}$$

if not, please give a right one.

Answer 1

The sum you have given is actually equal to $$X_1X_2+X_1X_3+X_2X_3$$ As noted in a comment, the sum you want is $$\sum_{i=1}^2X_iX_{i+1}$$

Answer 2

Your method is not correct (as saulspatz wrote). You can alternatively write the expression as a cyclic sum which cycles over ${x_1, x_2, x_3}$:

$$\left(\sum_{x_1, x_2, x_3} x_1x_2 \right) - x_3x_1$$.