Question 201264
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Not the condition<b><i>s</i></b>, the condition.


Let *[tex \Large \alpha] represent the single positive number, then *[tex \Large \alpha > 0].  Let *[tex \Large B = \{\beta_1,\beta_2,\cdots,\beta_{n-1},\beta_n\}] represent the set of negative numbers where *[tex \Large \beta_i < 0\ \forall\ \beta_i\ \in\ B].  Let *[tex \Large S] represent the sum of the elements of *[tex \Large B], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ S = \sum_{i=1}^n{b_i}]


And the questioned sum is then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha + S]


The required condition is then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha + S > 0 \ \ \Leftrightarrow\ \ |S| < \alpha]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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