Question

What is the sum of half + 3 quarters + 7 eights +15 sixteenths + 31 thirtytwoths + 63 sixtyfourths + 127 one-two-eighths + 255 two-five-sixths?

Answer 1

\[\frac{1}{2}+\frac{3}{4}+\frac{7}{8} +\frac{15}{16} +\frac{31}{32} +\text{ }\frac{63}{64}+\frac{127}{128} +\frac{255}{256}=\frac{1793}{256}=7\frac{1}{256} \]

Answer 2

nice robtobey, you did it first. . . :-)

Answer 3

Thank you for the medal.

Answer 4

\[1/2+3/4+7/8+15/16+31/32+63/64+127/128+256/256\]You know, you could have just said\[\sum_{n=1}^{8}(2^{n}-1)/2^{n}\]
but yeah the answer would be 1793/256