Question

Tính:

A = 8.(3²+1).(3⁴+1)...(3¹⁶+1)

Answer 1

\(A=8.\left(3^2+1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^4-1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^8-1\right)....\left(3^{16}+1\right)\\ =\left(3^{16}-1\right)\left(3^{16}+1\right)\\ =3^{32}-1\)

Answer 2

A = 8.(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)

= (3² - 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)

= (3⁴ - 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)

= (3⁸ - 1)(3⁸ + 1)(3¹⁶ + 1)

= (3¹⁶ - 1)(3¹⁶ + 1)

= 3³² - 1