作业帮设数列{an}和{bn}满足a1=b1=6,a2=b2=4,a3=b3=3 ,且数列{an+1-an}是等差数列
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设数列{an}和{bn}满足a1=b1=6,a2=b2=4,a3=b3=3 ,且数列{an+1-an}是等差数列
设数列{an}和{bn}满足a1=b1=6,a2=b2=4,a3=b3=3 ,且数列{a(n+1)-an}是等差数列,{bn-2}是等比数列
(2)设{nbn}的前n项和为Sn,求Sn的表达式
(3)数列{Cn}满足Cn=an*(b(n+2)-2),求数列{Cn}的最大项
设数列{an}和{bn}满足a1=b1=6,a2=b2=4,a3=b3=3 ,且数列{a(n+1)-an}是等差数列,{bn-2}是等比数列
(2)设{nbn}的前n项和为Sn,求Sn的表达式
(3)数列{Cn}满足Cn=an*(b(n+2)-2),求数列{Cn}的最大项
∵数列{a(n+1)-an}是等差数列
∴a2-a1=d=-2
∴an=6-2(n-1)=8-2n
∵{bn-2}是等比数列
∴q=b2 -2/b1 -2=1/2
∴bn-2=4乘以1/2^(n-1)
∴bn=2^(3-n) +2
∵nbn=n*2^(3-n) +2n
∴Sn=b1+b2+b3+...+bn=[1*2^2 +2*2^1 +3*2^0 +...+n*2^(3-n)]+[2n+2n(n-1)/2]
∴设 Tn=[1*2^2 +2*2^1 +3*2^0 +...(n-1)*2^(4-n) +n*2^(3-n)].[1]
2Tn=[1*2^3 +2*2^2 +3*2^1 +4*2^0 +...+(n-1)*2^(5-n)+n*2^(4-n)].[2]
[2]-[1]=Tn=[2^3+2^2+2^1+2^0+...+2^(4-n)]-n*2^(3-n)= 8(1-2^n)/1-2 - n*2^(3-n)
∴Sn=8(1-2^n)/1-2 - n*2^(3-n)) + [2n+2n(n-1)/2]
(3)Cn=an*(b(n+2)-2)=(8-2n) * 2^(1-n)
∴当n取得最小1时,8-2n=6为最大且2^(1-n)在n≥1中为单调减函数,即n=1时2^(1-n)=1为最大
∴Cn(MAX)=6
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∴a2-a1=d=-2
∴an=6-2(n-1)=8-2n
∵{bn-2}是等比数列
∴q=b2 -2/b1 -2=1/2
∴bn-2=4乘以1/2^(n-1)
∴bn=2^(3-n) +2
∵nbn=n*2^(3-n) +2n
∴Sn=b1+b2+b3+...+bn=[1*2^2 +2*2^1 +3*2^0 +...+n*2^(3-n)]+[2n+2n(n-1)/2]
∴设 Tn=[1*2^2 +2*2^1 +3*2^0 +...(n-1)*2^(4-n) +n*2^(3-n)].[1]
2Tn=[1*2^3 +2*2^2 +3*2^1 +4*2^0 +...+(n-1)*2^(5-n)+n*2^(4-n)].[2]
[2]-[1]=Tn=[2^3+2^2+2^1+2^0+...+2^(4-n)]-n*2^(3-n)= 8(1-2^n)/1-2 - n*2^(3-n)
∴Sn=8(1-2^n)/1-2 - n*2^(3-n)) + [2n+2n(n-1)/2]
(3)Cn=an*(b(n+2)-2)=(8-2n) * 2^(1-n)
∴当n取得最小1时,8-2n=6为最大且2^(1-n)在n≥1中为单调减函数,即n=1时2^(1-n)=1为最大
∴Cn(MAX)=6
好辛苦好辛苦好辛苦好辛苦.啊 啊啊啊啊啊啊暗暗暗暗啊啊啊啊啊啊 .啊啊啊啊 啊啊啊啊啊啊啊啊啊啊啊啊暗暗啊暗暗啊暗暗啊啊啊啊啊暗暗暗暗 .完.（看上面时间..）
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