1/2+1/4+1/8+1/16+1/32+...+1/256简便运算

来源：学生作业帮助网编辑：六六作业网时间：2024/12/25 23:57:18

1/2+1/4+1/8+1/16+1/32+...+1/256简便运算1/2+1/4+1/8+1/16+1/32+...+1/256简便运算1/2+1/4+1/8+1/16+1/32+...+1/25

1/2+1/4+1/8+1/16+1/32+...+1/256简便运算
1/2+1/4+1/8+1/16+1/32+...+1/256简便运算

1/2+1/4+1/8+1/16+1/32+...+1/256简便运算
1/2+1/4+1/8+1/16+1/32+...+1/256
=1/2+1/4+1/8+1/16+1/32+...+1/256+1/256-1/256
=1/2+1/4+1/8+1/16+1/32+...+1/128+1/128-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/256
=1/2+1/4+1/8+1/16+1/32+1/32-1/256
=……
=1-1/256=255/256

S=1/2+1/4+1/8+...1/256
1/2*S=1/4+1/8+1/16+...+1/256+1/512
两个式子相减,得
1/2*S=1/2-1/512
1/2+1/4+1/8+1/16+1/32+...+1/256
=255/256