1-1/2-1/4-1/8-1/16-…… -1 / 256 =? Calculation process and law

1-1/2-1/4-1/8-1/16-…… -1 / 256 =? Calculation process and law

1-1/2-1/4-1/8-1/16-…… -1/256=1-（1/2+1/4+1/8+1/16-…… +1/256）=1-（1-1/2+1/2-1/4+1/4-1/8+…… -1 / 128 + 1 / 128-1 / 256) = 1 - (1-1 / 256) = 1-255 / 256 = 1 / 256. The secret of this calculation is the split term cancellation, which is to split 1 / 2 into 1-1 / 2 and 1 / 4 into

1-2 / 1-4 / 1-8 / 1 / 256
I have to hand it in tomorrow

1-1/2-1/4-1/8-...-1/256
=1-(1-1/2)-(1/2-1/4)-(1/4-1/8)-...-(1/128-1/256)
=1-1+1/2-1/2+1/4-1/4+1/8-.-1/128+1/256
=1/256

0.75: 1 (simplification) fast

3：4