计算(3+1)(3^2+1)(3^4+1)(3^8+1)+1,结果用幂的形式表示

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计算(3+1)(3^2+1)(3^4+1)(3^8+1)+1,结果用幂的形式表示

计算(3+1)(3^2+1)(3^4+1)(3^8+1)+1,结果用幂的形式表示
计算(3+1)(3^2+1)(3^4+1)(3^8+1)+1,结果用幂的形式表示

计算(3+1)(3^2+1)(3^4+1)(3^8+1)+1,结果用幂的形式表示
(3+1)(3^2+1)(3^4+1)(3^8+1)+1
=1/2(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)+1
=1/2(3^2-1)(3^2+1)(3^4+1)(3^8+1)+1
=1/2(3^4-1)(3^4+1)(3^8+1)+1
=..
=1/2*3^16-1/2+1
=1/2*3^16+1/2

(3+1)(3^2+1)(3^4+1)(3^8+1)+1
=1/2(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)+1
=1/2(3^2-1)(3^2+1)(3^4+1)(3^8+1)+1
=1/2(3^4-1)(3^4+1)(3^8+1)+1
=1/2(3^8-1)(3^8+1)+1
=1/2(3^16-1)+1
=1/2×3^16+1/2
连续应用平方差公式(a+b)(a-b)=a²-b²