It is known that the sum of the first n terms of the sequence an = 1 / (3 ^ n-n-1) is SN. It is proved that Sn < 2 holds for any n ∈ n +

a1=1/(3-1-1)=1a(n+1)/an=(3ⁿ-n-1)/[3^(n+1)-(n+1)-1]=(1/3)[3^(n+1)-3n-3]/[3^(n+1)-(n+1)-1]=(1/3)[3^(n+1)-(n+1)-1-2n-1]/[3^(n+1)-(n+1)-1]=(1/3){1 -(2n+1)/[3^(n+1)-(n+1)-1]}=1/3 - (2n+1)/[3^(n+2)-3(...

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