n=1时,a1=S1=2a1-2
a1=2
n≥2时,an=Sn-S(n-1)=2an-2-2a(n-1)+2
an=2a(n-1)
an/a(n-1)=2,为定值,数列{an}是以2为首项,2为公比的等比数列.
an=2ⁿ
Tn=a1b1+a2b2+...+anbn=3×2+5×2²+7×2³+...+(2n+1)×2ⁿ
2Tn=3×2²+5×2³+...+(2n-1)×2ⁿ+(2n+1)×2^(n+1)
Tn-2Tn=-Tn=3×2+2×2²+2×2³+...+2×2ⁿ-(2n+1)×2^(n+1)
=2×(2+2²+...+2ⁿ) -(2n+1)×2^(n+1) +2
=2×2×(2ⁿ-1)/(2-1)-(2n+1)×2^(n+1) +2
=(1-2n)×2^(n+1) -2
Tn=(2n-1)×2^(n+1) +2