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:

xSum
11/2
23/4
37/8
415/16
531/32
663/64
7127/128
8255/256
9511/512
101023/1024

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