设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求{nan}的前n项Tn设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求a1,a2并求数列{an}的通项公式,求{nan}的前n项Tn
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![设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求{nan}的前n项Tn设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求a1,a2并求数列{an}的通项公式,求{nan}的前n项Tn](/uploads/image/z/5126208-24-8.jpg?t=%E8%AE%BEsn%E4%B8%BA%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C%E5%B7%B2%E7%9F%A5a1%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C2an-a1%3DS1%2ASn%E6%B1%82%7Bnan%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9Tn%E8%AE%BEsn%E4%B8%BA%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C%E5%B7%B2%E7%9F%A5a1%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C2an-a1%3DS1%2ASn%E6%B1%82a1%2Ca2%E5%B9%B6%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%2C%E6%B1%82%7Bnan%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9Tn)
设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求{nan}的前n项Tn设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求a1,a2并求数列{an}的通项公式,求{nan}的前n项Tn
设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求{nan}的前n项Tn
设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求a1,a2并求数列{an}的通项公式,求{nan}的前n项Tn
设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求{nan}的前n项Tn设sn为数列an的前n项和,已知a1不等于0,2an-a1=S1*Sn求a1,a2并求数列{an}的通项公式,求{nan}的前n项Tn
n=1时,2a1-a1=a1=S1S1=a1²
a1²-a1=0 a1(a1-1)=0
a1=0(舍去)或a1=1
n≥2时,2an-a1=2an-1=S1Sn=Sn
Sn=2an -1
an=Sn-S(n-1)=2an-1-2a(n-1)+1=2an-2a(n-1)
an=2a(n-1) an/a(n-1)=2,为定值,数列{an}是以1为首项,2为公比的等比数列.
an=1×2^(n-1)=2^(n-1)
n=1时,a1=2^0=1,同样满足通项公式,数列{an}的通项公式为an=2^(n-1)
a2=2^1=2
nan=n×2^(n-1)
Tn=1×1+2×2+3×2²+...+n×2^(n-1)
2Tn=1×2+2×2²+...+(n-1)×2^(n-1)+n×2ⁿ
Tn-2Tn=-Tn=1+2+...+2^(n-1)-n×2ⁿ
=1×(2ⁿ-1)/(2-1)-n×2ⁿ
=(1-n)×2ⁿ -1
Tn=(n-1)×2ⁿ +1