依題意得
Sn=4×2^2+7×2^3+10×2^4+…+(3n+1)×2^(n+1)
所以等式左右乘以等比數(shù)列的公比2,得：
2Sn=4×2^3+7×2^4+10×2^5+…+(3n+1)×2^(n+2)
所以2Sn-Sn=Sn=-4×2^2-[3×2^3+3×2^4+…+3×2^(n+1)]+(3n+1)×2^(n+2)
=-16-3[2^3+2^4+2^5+…+2^(n+1)]+(3n+1)×2^(n+2)
=-16-3[-2^3+2^(n+2)]+(3n+1)×2^(n+2)
整理得
=(3n-2)×2^(n+2)+8
已驗(yàn)算