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!

Back to Index Page Back to Math Trick Menu