1.a, b, c成等差數(shù)列,a, c, b, 成等比數(shù)列
2b=a+c,
c^2=ab
則：ab=(2b-a)^2
(a-b)(a-4b)=0
a,b,c是互不相等的實(shí)數(shù)
則：a/b=4
2.{an}是等比數(shù)列
log2a2+log2a4+log2a8+loga10=log2（a2*a4*a8a10）=log2（a6^4)
a3*a6*a9=a6^3=4
a6=4^(1/3)
log2（a6^4)=log2[4^(4/3)]=8/3
3.
(1)Sn=2n^2
S(n-1)=2(n-1)^2
Sn-S(n-1)=an=4n-2
a1=b1=2,
因?yàn)閎2(a2-a1)=b1
則：b2=1/2
{bn}為等比數(shù)列,
公比q=1/4
則：bn=1/2^(2n-3)
(2)cn=an/bn=(4n-2)*[2^(2n-3)]=(2n-1)*2^(2n-2)
Tn=1*2^0+3*2^2+5*2^4+...+(2n-1)*2^(2n-2)
4Tn=1*2^2+3*2^4+5*2^6+...+(2n-1)*2^(2n)
相減得：
3Tn=-1*2^0-2*2^2-2*2^4-...-2*2^(2n-2)+(2n-1)*2^(2n)
3Tn=-1-2*[2^2+2^4+...+2^(2n-2)]+(2n-1)*2^(2n)
3Tn=-1-2*4*[1-2^(2n-2)]/(-3)
Tn=-1+8*[1-2^(2n-2）]
4.題目錯(cuò)了吧?應(yīng)該是這個(gè)吧
已知,-l＜a+b ＜3且2＜a-b ＜4,則2a+3b 的范圍是 ?
設(shè)x（a+b）+y(a-b)=2a+3b
則：x+y=2
x-y=3
x=5/2,y=-1/2
x（a+b)=5/2（a+b)
-5/2＜5/2(a+b) ＜15/2
2＜a-b ＜4
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