计算 (3-1)(3^50+3^49+3^48+A+3^2+3+1)

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计算 (3-1)(3^50+3^49+3^48+A+3^2+3+1)
计算 (3-1)(3^50+3^49+3^48+A+3^2+3+1)

计算 (3-1)(3^50+3^49+3^48+A+3^2+3+1)
3^50+3^49+3^48+A+3^2+3+1 为等比数列求和
S=(1-3^50*3)/(1-3)=(3^51-1)/2
(3-1)(3^50+3^49+3^48+A+3^2+3+1)
=2*(3^51-1)/2
=3^51-1

等比数列求和
(3-1)(3^50+3^49+3^48+A+3^2+3+1)=(3-1)(1-3^51)/(1-3)=3^51-1

a1=1,q=3,n=51
Sn=a1(1-q^n)/(1-q)=(1-3^51)/(1-3)
(3-1)(3^50+3^49+3^48+A+3^2+3+1)=(3-1)Sn=3^51-1