求教几道数学题！！

Warrengxt

If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?




I.  1/8
II.  1/9
III.  1/10




A.None

B.I only
C.III only

D.II and III only

E.I, II, and III



A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?


A.20
B.36
C.48

D.60
E.84
这道题没太看懂，求解释

Tobelogical

第一题
1/100+1/99+...+1/91<1/100+(1/90)*9=11/100<1/9
同理
1/100+1/99+...+1/91>(1/100)*10=1/10

第二题
线性相关
所以设R为：y=ax+b
S: y=cx+d
得，
6a+b=30c+d
24a+b=60c+d
两式相减得
3a=5c

设所求值为H
Ha+b=100c+d
该式与第二式相减，得
(H-24)a=40c
带入关系式得H=48

第二题我解的好像比较麻烦。。。。

可爱小猪

第二题~

我理解的是，一个固定的值被R和S两种尺度衡量，R上的6和24对应S上的30和60，问你S上的100对应R上的多少~
R:----6------24----------X------
            18         X-24

S:----30-----60--------100----
             30         40

所以， 18/30=(X-24)/40  X=48

Tobelogical

对滴

Warrengxt

谢谢你们啦！very helpful！