(a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)(a^32+1) решите - вопрос №36226921214181161321 от 123291Duck 09.10.2020 16:06

Question

Математика: (a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)(a^32+1) решите

123291Duck · Answer

(a+1)(a²+1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)==(a+1)·(a-1)/(a-1)·(a²+1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)==1/(a-1)·(a²-1)(a²+1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)==1/(a-1)·(a⁴-1)(a⁴+1)(a⁸+1)(a¹⁶+1)(a³²+1)=1/(a-1)·(a⁸-1)(a⁸+1)(a¹⁶+1)(a³²+1)==1/(a-1)·(a¹⁶-1)(a¹⁶+1)(a³²+1)=1/(a-1)·(a³²-1)(a³²+1)=(a⁶⁴-1)/(a-1);...