# Super Summation 9

## The numerator of the sum will always be 1 less than the denominator!

__According to the table below, the sum will be equal to these fractions if __*x* is equal to these natural numbers:

x | Sum |

1 | 1/2 |

2 | 3/4 |

3 | 7/8 |

4 | 15/16 |

5 | 31/32 |

6 | 63/64 |

7 | 127/128 |

8 | 255/256 |

9 | 511/512 |

10 | 1023/1024 |

Obviously, the denominator is always equal to a power of **2**, but the numerator will be equal to the consecutive integer before that, every time! However, *x* can't be equal to a number that's less than **1**. You can't pick a non-integer for *x* either, because this is __summation.__

## Well, I guess there's no more to explain about this math trick, so I can keep this Web page short & sweet!

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© Derek Cumberbatch