sum of powers of two including fractions (original) (raw)

sum of powers of two including fractions Demonstration that the sum of powers of two from zero to a given power, inclusive, is 1 less than the next power of two, whereas the sum of powers of two from minus-infinity to a given power, inclusive, equals the next power of two by CMG Lee. 2⁰=1 2¹=2 2²=4 2³ = 8 2⁴ = 16 2⁵ = 32 2⁶ = 64 2⁷ = 128 2⁻¹ = 1/2 2⁻² = 1/4 2⁻³ = 1/8 2⁻⁴ = 1/16 2⁻⁵ = 1/32 2⁻⁶ = 1/64 ...