配电房土建图纸:【已知A=1/2^3 +1/(2^3+1) +1/(2^3+2) +… +1/(2^4-1),则A与1的大小关系是______】

来源:百度文库 编辑:神马品牌网 时间:2024/05/05 13:40:51
已知A=1/2^3 +1/(2^3+1) +1/(2^3+2) +… +1/(2^4-1),则A与1的大小关系是______

WHY??

从2^3到2^4-1一共8项

1/2^3 +1/(2^3+1) +1/(2^3+2) +… +1/(2^4-1)
<1/2^3 +1/2^3+ ……+1/2^3(8项1/2^3 )
=8/8
=1

所以 1/2^3 +1/(2^3+1) +1/(2^3+2) +… +1/(2^4-1)〈1

A=1/2^3 +1/(2^3+1) +1/(2^3+2) +… +1/(2^4-1)
=1/8+1/9+1/10+……+1/15
<1/8+1/8+1/8+……+1/8
=8*1/8
=1
---> A<1

汗....看不懂

1+1=2