Sn= 2+ 5×2+8×2^2+ .+(3n-1) ×2^n-1 ①
2Sn= 2×2+5×2^2 ……..+〔3(n-1)-1〕×2^n-1 + (3n-1) 2^n ②
错位相减
①-②得
-Sn= 2+3×2+3×2^2 +……+3×2^n-1 - (3n-1) 2^n
Sn= (3n-1) 2^n – 3(2+22 +……+2n-1 )-2
= (3n-1) 2^n -2-3×〔2×(1-2^n-1 ) 〕/(1-2)
=4+(3n-4)× 2^n
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