数列题,最好发图,
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数列题,最好发图,数列题,最好发图, 数列题,最好发图,α+β=-[-a(n+1)]/an=a(n+1)/anαβ=1/an6α-2αβ+6β=6(α+β)-2αβ=36a(n+1)/an-
数列题,最好发图,
数列题,最好发图,
数列题,最好发图,
α+β=-[-a(n+1)]/an=a(n+1)/an
αβ=1/an
6α-2αβ+6β=6(α+β)-2αβ=3
6a(n+1)/an-2×1/an=3
a(n+1)=1/2an+1/3
a(n+1)-2/3=1/2(an-2/3)
[a(n+1)-2/3]/(an-2/3)=1/2
a1-2/3=7/6-2/3=1/2
数列{an-2/3}是以1/2为首项,以1/2为公比的等比数列
an-2/3=1/2×(1/2)^(n-1)
an=(1/2)^n+2/3
nan=n·(1/2)^n+2/3·n
数列{n·(1/2)^n}的前n项和记为Rn,数列{2/3·n}的前n项和记为Sn
Rn=1×(1/2)^1+2×(1/2)^2+3×(1/2)^3+……+n×(1/2)^n
1/2Rn=1×(1/2)^2+2×(1/2)^3+3×(1/2)^4+……+n×(1/2)^(n+1)
Rn-1/2Rn=1×(1/2)^1+1×(1/2)^2+1×(1/2)^3+1×(1/2)^4+……+1×(1/2)^n-n×(1/2)^(n+1)
1/2Rn=1/2[1-(1/2)^n]/(1-1/2)-n×(1/2)^(n+1)
Rn=2-(n+2)(1/2)^n
Sn=2/3×(1+2+3+……+n)=n(n+1)/3
Tn=Rn+Sn=2-(n+2)(1/2)^n+n(n+1)/3．