Question 192686
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^n{i} = \frac{(1 + n)n}{2}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{(1 + n)n}{2} = 4950]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \  (1 + n)n = 9900]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  n^2 + n - 9900 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  (n + 100)(n - 99) = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n = -100 \ \text{or}\ n = 99]


Exclude -100 as an extraneous root (not a natural number).  <b><i>n</i> = 99</b>


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