计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 21:40:14
计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
设a=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
2a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128 (上式乘2)
则
2a-a=a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 )
=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1-1/256
=255/256
255/256
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=128/256+64/256+32/256+16/256+8/256+4/256+2/256+1/256
=255/256
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1-1/2+1/2-1/4+1/4-1/8....
=1-1/256
=255/256
等比数列的求解
可以利用公式求的
这道题目我们可以得到(1/2 - (1/2)^n+1)/1/2=1-1/2^n
如果n有限,代入计算就可以了
假如n的无穷大,我们可以忍为结果就是1了
128/256+64/256+32/256+16/256+4/256+2/256+1/256=128+64+32+16+8+4+2+1/256=255/256