Question

数学题目，求回答

二分之一加四分之二加八分之三加十六分之四加三十二分之五加六十四分之六加一百二十八分之七加二百五十六分之八加五百一十二分之九
这题我搞不懂
我这个上面打不上数字，求你们麻烦一下，换成数字写在纸上，要巧算的哦，最好有解析，我们刚考完期中

Answer 1

设s=1/2+2/4+3/8+4/16+5/32+6/64+7/128+8/256+9/512
则2s=1+1 +3/4+4/8+5/16+6/32+7/64+8/128+9/256
2s-s=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256-9/512
=(1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256)-1/256-9/512
=2-(1/256+9/512)
=2-11/512
=1又501/512

Answer 2

设s=1/2+2/4+3/8+4/16+5/32+6/64+7/128+8/256+9/512
则2s=1 +1/2+3/4+4/8+5/16+6/32+7/64+8/128+9/256
2s-s=1+1/4+1/8+1/16+1/32+1/64+1/128+1/256-9/512=1+1/2-1/4+1/4-1/8+。。。。+1/128-1/256-9/512=1+1/2-1/256-9/512=1又245/512

Answer 3

解：设s=1/2+2/4+3/8+4/16+5/32+6/64+7/128+8/256+9/512
则2s=1+1 +3/4+4/8+5/16+6/32+7/64+8/128+9/256
2s-s=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256-9/512
=(1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256)-1/256-9/512
=2-(1/256+9/512)
=2-11/512
=1又501/512