设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指
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![设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指](/uploads/image/z/6081969-57-9.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%3Dn%5E2%2C%E6%95%B0%E5%88%97%7Bbn%7D%E6%BB%A1%E8%B6%B3bn%3Dan%2Fan%2Bm%28m%E5%B1%9E%E4%BA%8EN%2A%29%2C%EF%BC%881%EF%BC%89%E8%8B%A5b1%2Cb2%2Cb8%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E8%AF%95%E6%B1%82m%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8m%2C%E4%BD%BF%E5%BE%97%E6%95%B0%E5%88%97%EF%BD%9Bbn%EF%BD%9D%E4%B8%AD%E5%AD%98%E5%9C%A8%E6%9F%90%E9%A1%B9bt%E6%BB%A1%E8%B6%B3b1%2Cb4%2Cbt%28t%E5%B1%9E%E4%BA%8EN%2A%2Ct%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E5%29%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%3F%E8%8B%A5%E5%AD%98%E5%9C%A8%2C%E6%8C%87)
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设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指
设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成
等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指出m的个数,若不存在,说明理由.
设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指
n>=2
Sn=n^2
Sn-1=(n-1)^2
Sn-Sn-1=n^2-(n-1)^2=2n-1=an
(n>=2)
n=1,a1=S1=1,
a1=2-1=1
an=2n-1(n,N*)
bn=an/(an+m)=(2n-1)/(2n-1+m)
b1=1/(1+m),b2=3/(3+m),b8=15/(15+m)
b2^2=b1b8
9/(3+m)^2=1/(1+m)*15/(15+m)
3/(3+m)^2=5/(1+m)(15+m)
3(1+m)(15+m)=5(3+m)^2
3(15+16m+m^2)=5(9+6m+m^2)
45+48m+3m^2=45+30m+5m^2
2m^2-18m=0
m^2-9m=0
m=0,m=9
m,N*
m=9
(2)若存在
b1=1/(1+m),b4=7/(7+m),bt=(2t-1)/(2t-1+m)
2b4=b1+bt
2*7/(7+m)=1/(1+m)+(2t-1)/(2t-1+m)
14/(7+m)=1/(1+m)+(2t-1)/(2t-1+m)
14(1+m)(2t-1+m)=(7+m)(2t-1+m)+(2t-1)(7+m)(1+m)
设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指
设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成
等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指出m的个数,若不存在,说明理由.
设数列{an}的前n项和Sn=n^2,数列{bn}满足bn=an/an+m(m属于N*),(1)若b1,b2,b8成等比数列,试求m的值;(2)是否存在m,使得数列{bn}中存在某项bt满足b1,b4,bt(t属于N*,t大于等于5)成等差数列?若存在,指
n>=2
Sn=n^2
Sn-1=(n-1)^2
Sn-Sn-1=n^2-(n-1)^2=2n-1=an
(n>=2)
n=1,a1=S1=1,
a1=2-1=1
an=2n-1(n,N*)
bn=an/(an+m)=(2n-1)/(2n-1+m)
b1=1/(1+m),b2=3/(3+m),b8=15/(15+m)
b2^2=b1b8
9/(3+m)^2=1/(1+m)*15/(15+m)
3/(3+m)^2=5/(1+m)(15+m)
3(1+m)(15+m)=5(3+m)^2
3(15+16m+m^2)=5(9+6m+m^2)
45+48m+3m^2=45+30m+5m^2
2m^2-18m=0
m^2-9m=0
m=0,m=9
m,N*
m=9
(2)若存在
b1=1/(1+m),b4=7/(7+m),bt=(2t-1)/(2t-1+m)
2b4=b1+bt
2*7/(7+m)=1/(1+m)+(2t-1)/(2t-1+m)
14/(7+m)=1/(1+m)+(2t-1)/(2t-1+m)
14(1+m)(2t-1+m)=(7+m)(2t-1+m)+(2t-1)(7+m)(1+m)