Question

算式求值的题，如1/4+3/8+7/16+15/32+.+511/1024=

Answer 1

引用cn#aBkBLaaGBQ的回答：
1/4+3/8+7/16+15/32+...+511/1024
=[(1/2)-(1/4)]+[(1/2)-(1/8)]+[(1/2)-(1/16)]+[(1/2)-(1/32)]+..+[(1/2)-(1/1024)]
=(1/2)*256-{(1/4)*[1-(1/2)^256]/(1/2)}
=128-(1/2)+(1/2)^257
=127.5+2^(-257)

=[(1/2)-(1/4)]+[(1/2)-(1/8)]+[(1/2)-(1/16)]+[(1/2)-(1/32)]+..+[(1/2)-(1/1024)]

=9*（1/2)-[(1/4)+(1/8)]+(1/16)]+...(1/1024)]
=9*（1/2)-[(1/2)+(1/4)+(1/8)]+(1/16)]+...(1/1024)] +(1/2) 此处为了方便计算加入1/2，
=9/2-[(1/2-1/1024*1/2）/ (1-1/2)] +1/2 等比数列求和
=9/2-(1-1/1024)+1/2
=9+1/1024

Answer 2

1/4+3/8+7/16+15/32+...+511/1024
=[(1/2)-(1/4)]+[(1/2)-(1/8)]+[(1/2)-(1/16)]+[(1/2)-(1/32)]+..+[(1/2)-(1/1024)]
=(1/2)*256-{(1/4)*[1-(1/2)^256]/(1/2)}
=128-(1/2)+(1/2)^257
=127.5+2^(-257)