Question

So sánh: 4.(3²+1).(3⁴+1).(3⁸+1)........(3⁶⁴+1) và 3¹²⁸-1

Answer 1

\(S=4\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)

\(\left(3^2-1\right)S=4\cdot\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)

\(8S=4\cdot\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)

\(2S=\left(3^8-1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)

...

\(2S=3^{128}-1\)

Vậy S < 3¹²⁸ - 1