potęgi róza: Zapisz w postaci potęgi 1+(2+1)*(2²+1)*(2⁴+1)*(2⁸+1)*(2¹⁶+1)*(2³²+1)

jc: Mnożymy przez (2−1)=1. =1 + (2−1)(2+1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1) =1 + (2²−1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1) =1 + (2⁴−1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1) =1 + (2⁸−1)(2⁸+1)(2¹⁶+1)(2³²+1) =1 + (2¹⁶−1)(2¹⁶+1)(2³²+1) =1 + (2³²−1)(2³²+1) =1 + 2⁶⁴−1=2⁶⁴ lub od razu jak ktoś widzi 1 + (1+2+4+8+...+2³²)=2⁶⁴