新狗求问 在线等 急~~~

fangpyj8906

DS：1+x+x^2+x^3+x^4 >1/（1-x）?

第一个条件 x>0

第二个条件 x<1

脑子锈了，求高人指点

fangpyj8906

自己顶

sdcar2010

The short answer is C.

The long answer is to use 等比数列求和公式 to simplify the sum and then you can do some analysis.

lsbhome

等比数列 求和公式 Sn=a1(1-q^n)/(1-q)

左边是等比数列，q=x，S5=(1-x^5)/(1-x)
即求证 (1-x^5)/(1-x)>1/(1-x)?
x≠1
x<1时，1-x>0, 1-x^5>1, x^5<0, x<0
x>1时，1-x<0, 1-x^5<1, X^5>0, x>1
所以 x<0或x>1时 左>右
同理可证 0<x<1 时 右>左

fangpyj8906

谢谢楼上的XDJM

joycelzh

The short answer is C.

The long answer is to use 等比数列求和公式 to simplify the sum and then you can do some analysis.

-- by 会员 sdcar2010 (2010/12/28 0:02:10)

sdcar2010

Then you use 0.1 and 2 as values for x for the equation and calculate 1+x+x^2+x^3+x^4; 1/(1-x).

when x = 0.1, 1+x+x^2+x^3+x^4 < 1/(1-x)
when x = 2, 1+x+x^2+x^3+x^4 >1/(1-x)

So when x >0, it is insufficient to decide which one is bigger.

这题我的解是A, 因为A就能解释了，不需要看B了.

The short answer is C.

The long answer is to use 等比数列求和公式 to simplify the sum and then you can do some analysis.

-- by 会员 sdcar2010 (2010/12/28 0:02:10)

-- by 会员 joycelzh (2010/12/28 7:26:22)

Jennyqu

用-1, 1/2, 和2带下就可以了。