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(2007上海,20)如果有窮數(shù)列,,…,(n為正整數(shù))滿足條件,我們稱其為“對(duì)稱數(shù)列”.例如,由組合數(shù)組成的數(shù)列就是“對(duì)稱數(shù)列”.

(1)設(shè)是項(xiàng)數(shù)為7的“對(duì)稱數(shù)列”,其中是等差數(shù)列,且.依次寫出的每一項(xiàng);

(2)設(shè)是項(xiàng)數(shù)為2k1(正整數(shù)k1)的“對(duì)稱數(shù)列”,且,,…,是首項(xiàng)為50,公差為-4的等差數(shù)列.記各項(xiàng)的和為.當(dāng)k為何值時(shí),取得最大值?并求出的最大值;

(3)對(duì)于確定的正整數(shù)m1,寫出所有項(xiàng)數(shù)不超過2m的“對(duì)稱數(shù)列”,使得依次是該數(shù)列中連續(xù)的項(xiàng);當(dāng)m1500時(shí),求其中一個(gè)“對(duì)稱數(shù)列”前2008項(xiàng)的和

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如果有窮數(shù)列a1,a2,a3,…,an(n∈N*)滿足a1=an,a2=an-1,…,an=a1,即ai=an-i+1(i=1,2,…n),則稱其為“對(duì)稱數(shù)列”.
(1)設(shè){bn}是項(xiàng)數(shù)為7的“對(duì)稱數(shù)列”,其中b1,b2,b3,b4是等差數(shù)列,且b1=2,b4=11,則數(shù)列{bn}的各項(xiàng)分別是______
(2)設(shè){Cn}是項(xiàng)數(shù)為2k-1(k∈N*,k>1)的“對(duì)稱數(shù)列”,其中Ck,Ck+1,…,C2k-1是首項(xiàng)為50,公差為-4的等差數(shù)列,記{Cn}各項(xiàng)和和為S2k-1,則S2k-1的最大值為______.

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如果有窮數(shù)列a1,a2,a3,…,an(n∈N*)滿足a1=an,a2=an-1,…,an=a1,即ai=an-i+1(i=1,2,…n),則稱其為“對(duì)稱數(shù)列”.
(1)設(shè){bn}是項(xiàng)數(shù)為7的“對(duì)稱數(shù)列”,其中b1,b2,b3,b4是等差數(shù)列,且b1=2,b4=11,則數(shù)列{bn}的各項(xiàng)分別是   
(2)設(shè){Cn}是項(xiàng)數(shù)為2k-1(k∈N*,k>1)的“對(duì)稱數(shù)列”,其中Ck,Ck+1,…,C2k-1是首項(xiàng)為50,公差為-4的等差數(shù)列,記{Cn}各項(xiàng)和和為S2k-1,則S2k-1的最大值為   

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(理)如果有窮數(shù)列a1,a2,a3,…,an(n為正整數(shù))滿足條件a1=an,a2=an-1,…,an=a1,即ai=an-i+1(i=1,2,…,n),我們稱其為“對(duì)稱數(shù)列”.例如,由組合數(shù)組成的數(shù)列,,…,就是“對(duì)稱數(shù)列”.

(1)設(shè){bn}是項(xiàng)數(shù)為7的“對(duì)稱數(shù)列”,其中b1,b2,b3,b4是等差數(shù)列,且b1=2,b4=11.依次寫出{bn}的每一項(xiàng).

(2)設(shè){cn}是項(xiàng)數(shù)為2k-1(正整數(shù)k>1)的“對(duì)稱數(shù)列”,其中ck,ck+1,…,c2k-1是首項(xiàng)為50,公差為-4的等差數(shù)列.記{cn}各項(xiàng)的和為S2k-1,當(dāng)k為何值時(shí),S2k-1取得最大值?并求出S2k-1的最大值.

(3)對(duì)于確定的正整數(shù)m>1,寫出所有項(xiàng)數(shù)不超過2m的“對(duì)稱數(shù)列”,使得1,2,22,…,2m-1依次是該數(shù)列中連續(xù)的項(xiàng);當(dāng)m>1 500時(shí),求其中一個(gè)“對(duì)稱數(shù)列”前2 008項(xiàng)的和S2008.

(文)如果有窮數(shù)列a1,a2,a3,…,am(m為正整數(shù))滿足條件a1=am,a2=am-1,…,am=a1,即ai=am-i+1(i=1,2,…,m),我們稱其為“對(duì)稱數(shù)列”.例如,數(shù)列1,2,5,2,1與數(shù)列8,4,2,2,4,8都是“對(duì)稱數(shù)列”.

(1)設(shè){bn}是7項(xiàng)的“對(duì)稱數(shù)列”,其中b1,b2,b3,b4是等差數(shù)列,且b1=2,b4=11.依次寫出{bn}的每一項(xiàng);

(2)設(shè){cn}是49項(xiàng)的“對(duì)稱數(shù)列”,其中c25,c26,…,c49是首項(xiàng)為1,公比為2的等比數(shù)列,求{cn}各項(xiàng)的和S;

(3)設(shè){dn}是100項(xiàng)的“對(duì)稱數(shù)列”,其中d51,d52,…,d100是首項(xiàng)為2,公差為3的等差數(shù)列,求{dn}前n項(xiàng)的和Sn(n=1,2,…,100).

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20、若有窮數(shù)列a1,a2…an(n是正整數(shù)),滿足a1=an,a2=an-1…an=a1即ai=an-i+1
(i是正整數(shù),且1≤i≤n),就稱該數(shù)列為“對(duì)稱數(shù)列”.
(1)已知數(shù)列{bn}是項(xiàng)數(shù)為7的對(duì)稱數(shù)列,且b1,b2,b3,b4成等差數(shù)列,b1=2,b4=11,試寫出{bn}的每一項(xiàng)
(2)已知{cn}是項(xiàng)數(shù)為2k-1(k≥1)的對(duì)稱數(shù)列,且ck,ck+1…c2k-1構(gòu)成首項(xiàng)為50,公差為-4的等差數(shù)列,數(shù)列{cn}的前2k-1項(xiàng)和為S2k-1,則當(dāng)k為何值時(shí),S2k-1取到最大值?最大值為多少?
(3)對(duì)于給定的正整數(shù)m>1,試寫出所有項(xiàng)數(shù)不超過2m的對(duì)稱數(shù)列,使得1,2,22…2m-1成為數(shù)列中的連續(xù)項(xiàng);當(dāng)m>1500時(shí),試求其中一個(gè)數(shù)列的前2008項(xiàng)和S2008

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