化简$$(a+1)(a^2+1)(a^4+1)\dots(a^{2^n}+1)$$

Question

Uniteasy Admin · Accepted Answer

$$(a+1)(a^2+1)(a^4+1)\dots({a^2}^n+1)$$
$$=\dfrac{(a^2-1)(a^2+1)(a^4+1)\dots({a^2}^n+1)}{a-1} $$
$$= \dfrac{(a^4-1)(a^4+1)\dots({a^2}^n+1)}{a-1}$$
$$= \dfrac{({a^2}^n-1) ({a^2}^n+1)}{a-1}$$
$$=\dfrac{{a^2}^{n+1}-1}{a-1} $$

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