Question

СРОЧНО!!!! Вычислите рационально: (4+1)*(4²+1)*(4⁴+1)*(4⁸+1)-1/3*4¹⁶

Answer 1

$(4+1)*(4^2+1)*(4^4+1)*(4^8+1)- \frac{1}{3} *4^{16}=$$=\frac{(4-1)(4+1)*(4^2+1)*(4^4+1)*(4^8+1)}{(4-1)} - \frac{1}{3} *4^{16}=$$=\frac{(4^2-1)*(4^2+1)*(4^4+1)*(4^8+1)}{3} - \frac{4^{16}}{3} =\frac{(4^4-1)*(4^4+1)*(4^8+1)}{3} - \frac{4^{16}}{3} =$$=\frac{(4^8-1)*(4^8+1)}{3} - \frac{4^{16}}{3} =\frac{4^{16}-1}{3} - \frac{4^{16}}{3} =\frac{4^{16}-1-4^{16}}{3} =- \frac{1}{3}$