已知数列{an}前n项和为sn=2^(n+2)-4 设Bn=an*log2(an) 求数列b的前n项和
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已知数列{an}前n项和为sn=2^(n+2)-4 设Bn=an*log2(an) 求数列b的前n项和
![已知数列{an}前n项和为sn=2^(n+2)-4 设Bn=an*log2(an) 求数列b的前n项和](/uploads/image/z/16740634-58-4.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%3D2%5E%28n%2B2%29-4+%E8%AE%BEBn%3Dan%2Alog2%EF%BC%88an%EF%BC%89+%E6%B1%82%E6%95%B0%E5%88%97b%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C)
a1=s1=2^(1+2)-4=4
sn=2^(n+2)-4
s(n-1)=2^(n+1)-4
an=sn-s(n-1)
an=2^(n+2)-4-[2^(n+1)-4]
=2^(n+2)-2^(n+1)
=2*2^(n+1)-2^(n+1)
=2^(n+1)
an=2^(n+1)
当n=1时,也符合
Bn=an*log2(an)
=2^(n+1)log2[2^(n+1)]
=(n+1)*2^(n+1)
b1=2*2^2
b2=3*2^3
.
bn=(n+1)*2^(n+1)
Sbn=b1+b2+b3+.+bn
=2*2^2+3*2^3+.+(n+1)*2^(n+1)
2Sbn=2*2^3+3*2^4+.+(n+1)^(n+2)
Sbn-2Sbn=2*2^2+2^3+2^4+.+2^(n+1)-(n+1)*2^(n+2)
-Sbn=8+8*[1-2^(n-1)]/(1-2)-(n+1)*2^(n+2)
-Sbn=8+8*[2^(n-1)-1]-(n+1)*2^(n+2)
-Sbn=8+8*2^(n-1)-8-(n+1)*2^(n+2)
-Sbn=8*2^(n-1)-(n+1)*2^(n+2)
-Sbn=2^(n+2)-(n+1)*2^(n+2)
Sbn=(n+1)*2^(n+2)-2^(n+2)
Sbn=(n+1-1)*2^(n+2)
Sbn=n*2^(n+2)
sn=2^(n+2)-4
s(n-1)=2^(n+1)-4
an=sn-s(n-1)
an=2^(n+2)-4-[2^(n+1)-4]
=2^(n+2)-2^(n+1)
=2*2^(n+1)-2^(n+1)
=2^(n+1)
an=2^(n+1)
当n=1时,也符合
Bn=an*log2(an)
=2^(n+1)log2[2^(n+1)]
=(n+1)*2^(n+1)
b1=2*2^2
b2=3*2^3
.
bn=(n+1)*2^(n+1)
Sbn=b1+b2+b3+.+bn
=2*2^2+3*2^3+.+(n+1)*2^(n+1)
2Sbn=2*2^3+3*2^4+.+(n+1)^(n+2)
Sbn-2Sbn=2*2^2+2^3+2^4+.+2^(n+1)-(n+1)*2^(n+2)
-Sbn=8+8*[1-2^(n-1)]/(1-2)-(n+1)*2^(n+2)
-Sbn=8+8*[2^(n-1)-1]-(n+1)*2^(n+2)
-Sbn=8+8*2^(n-1)-8-(n+1)*2^(n+2)
-Sbn=8*2^(n-1)-(n+1)*2^(n+2)
-Sbn=2^(n+2)-(n+1)*2^(n+2)
Sbn=(n+1)*2^(n+2)-2^(n+2)
Sbn=(n+1-1)*2^(n+2)
Sbn=n*2^(n+2)
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