Is the sum $$ \sum_{i=1}^{2}\sum_{j=1}^{2}x_i $$
equals to
$$\sum_{i=1}^{2}x_i ?$$
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What "sum of j=1 to j=2 of xI" means? – JiminP May 06 '13 at 07:50
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I meant x subscript I – MrHumphey May 06 '13 at 07:51
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Isn't it just $2x_i$? – JiminP May 06 '13 at 07:52
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you can use mathjax to format your math expressions.read this also when you post a question next time http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – lakshman May 06 '13 at 07:55
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Is this what you want to ask? – Mhenni Benghorbal May 06 '13 at 07:59
1 Answers
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\begin{align*} \left(\sum_{i=1}^2 x_i \right)\left(\sum_{j=1}^2 x_j \right) &= (x_1 + x_2)(x_1 + x_2) \\ &= x_1^2 + 2x_1 x_2 + x_2^2, \end{align*} unless I'm missing something ...
EDIT:
After reading your edited question, I see now what you are asking: $$ \sum_{i=1}^2 \sum_{j=1}^2 x_i = \sum_{i=1}^2 x_i \sum_{j=1}^2 1 = 2\sum_{i=1}^2 x_i = 2(x_1 + x_2). $$ You can take $x_i$ out of the sum on $j$ because it doesn't depend on $j$.
Rookatu
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