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| Both sides previous revision Previous revision | Last revision Both sides next revision | ||
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rational_numbers [2016/04/23 13:41] nikolaj |
rational_numbers [2016/04/23 13:49] nikolaj |
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| For all $m$ | For all $m$ | ||
| - | $\dfrac{1}{x}=1 + \sum_{k=1}^m (1-x)^k + \dfrac{1}{x} (1-x)^{m+1}$ | + | ^ $\sum_{k=0}^m x^k = \dfrac{1}{1-x}(1-x^{m+1})$ ^ |
| + | ^ $\sum_{k=0}^m (1-y)^k = \dfrac{1}{y}-\dfrac{1}{y}(1-y)^{m+1}$ ^ | ||
| == Logic == | == Logic == | ||
