设等差数列{an}的公差为d(d>0),且满足:a2×a5=55,a2+a8=221)若数列{bn}的前n项和为an,数列{bn}和数列{cn}满足bn=cn/n,求数列{cn}的前n项和Sn
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![设等差数列{an}的公差为d(d>0),且满足:a2×a5=55,a2+a8=221)若数列{bn}的前n项和为an,数列{bn}和数列{cn}满足bn=cn/n,求数列{cn}的前n项和Sn](/uploads/image/z/8827573-13-3.jpg?t=%E8%AE%BE%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%85%AC%E5%B7%AE%E4%B8%BAd%EF%BC%88d%EF%BC%9E0%EF%BC%89%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%EF%BC%9Aa2%C3%97a5%3D55%2Ca2%2Ba8%3D221%EF%BC%89%E8%8B%A5%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAan%2C%E6%95%B0%E5%88%97%7Bbn%7D%E5%92%8C%E6%95%B0%E5%88%97%7Bcn%7D%E6%BB%A1%E8%B6%B3bn%3Dcn%2Fn%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bcn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn)
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设等差数列{an}的公差为d(d>0),且满足:a2×a5=55,a2+a8=221)若数列{bn}的前n项和为an,数列{bn}和数列{cn}满足bn=cn/n,求数列{cn}的前n项和Sn
设等差数列{an}的公差为d(d>0),且满足:a2×a5=55,a2+a8=22
1)若数列{bn}的前n项和为an,数列{bn}和数列{cn}满足bn=cn/n,求数列{cn}的前n项和Sn
设等差数列{an}的公差为d(d>0),且满足:a2×a5=55,a2+a8=221)若数列{bn}的前n项和为an,数列{bn}和数列{cn}满足bn=cn/n,求数列{cn}的前n项和Sn
a2+a8=22,2a5=22,a5=11,代入a2×a5=55得a2=5
3d=a5-a2=6,d=2
an=2n+1
b1=a1=3,
bn=an-a(n-1)=2,n>1
cn=nbn
c1=b1=3
cn=2n,n>1
S1=c1=3
Sn=3+4+6+8+…+2n=3+(n-1)(2n+4)/2=(n-1)(n+2)+3,n>1
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