Proof: (1 + A + A ^ 2 +...) +a^n）^2-a^n=(1+a+a^2+… +a^n-1)(1+a+a^2+… +A ^ n + 1), where is n natural number

Right = (1 + A + A ^ 2 +...) +a^n-1)(1+a+a^2+… +a^n+1)
=[1+a+a^2+...+a^n -a^n]*[1+a+...+a^n + a^(n+1)]
=(1+a+a^2+...+a^n)^2 - a^n(1+a+...+a^n+a^(n+1)) + a^(n+1)(1+a+...+a^n)
=(1+a+a^2+...+a^n)^2 - (a^n+a^(n+1)+...+a^(2n+1)) + (a^(n+1) +a^(n+2)+...+a^(2n+1))
=(1+a+a^2+...+a^n)^2 - a^n
=Left

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