Sn＝213+419+6127+…+(2n+13n)=n(n+1)+1−(13)n2n(n+1)+1−(13)n2．

Question

Sn＝2(1)/(3)+4(1)/(9)+6(1)/(27)+…+(2n+(1)/(3n))=

n(n+1)+(1−((1)/(3))n)/(2)

n(n+1)+(1−((1)/(3))n)/(2)

．

Answer 1

Sn＝2(1)/(3)+4(1)/(9)+6(1)/(27)+…(2n+(1)/(3n))
=(2+4+6+…+2n)+((1)/(3)+(1)/(9)+…+(1)/(3n))
=(2+2n)/(2)×n+((1)/(3)(1−(1)/(3n)))/(1−(1)/(3))
=n(n+1)+(1−((1)/(3))n)/(2)
故答案为：n(n+′1)+(1−((1)/(3))n)/(2)