以知an=2n+1,bn=(1/3)^n ,求:Sn=a1b1+a2b2+a3b3+.anbn,的值.
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以知an=2n+1,bn=(1/3)^n ,求:Sn=a1b1+a2b2+a3b3+.anbn,的值.
以知an=2n+1,bn=(1/3)^n ,求:Sn=a1b1+a2b2+a3b3+.anbn,的值.
以知an=2n+1,bn=(1/3)^n ,求:Sn=a1b1+a2b2+a3b3+.anbn,的值.
sn=3*(1/3)^1+5*(1/3)^2+7*(1/3)^3+.+(2n+1)*(1/3)^n
1/3*sn=3*(1/3)^2+5*(1/3)^3+7*(1/3)^4+.+(2n+1)*(1/3)^(n+1)
sn-1/3*sn
=3*(1/3)^1+2*(1/3)^2+2*(1/3)^3+2*(1/3)^4+.+2*(1/3)^n-(2n+1)*(1/3)^(n+1)
=1+2*1/9*[1-(1/3)^(n-1)]/(1-1/3)-(2n+1)*(1/3)^(n+1)
=1+1/3-(1/3)^n-(2n+1)*(1/3)^(n+1)
=4/3-(1/3)^n-(2n+1)/3*(1/3)^n
=4/3-(1/3)^n[1+(2n+1)/3]
=4/3-(1/3)^n(2n+5)/3
2sn/3=4/3-(1/3)^n(2n+5)/3
2sn=4-(1/3)^n(2n+5)
sn=2-(2n+5)(1/3)^n/2
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