1/2+1/4+1/8+1/16+.+1/512的简便计算

Answer 1

有学过等比数列吗?
没学过就用这个方法吧
1/2+1/4+1/8+1/16+.+1/512 = 1/2+1/4+1/8+1/16+.+1/512 +1 -1 //加1再减1
= -1+1/2+1/4+1/8+1/16+.+1/512 +1
然后简单了
-1+1/2=-1/2
-1/2+ 1/4=-1/4
……
最后 = -1/512+1= 511/512