Question

[Nguyễn Khả Hân]

So sánh 

(9+1)(9^2+1)(9^4+1)(9^8+1)(9^16+1)(9^32+1) và 9^64-1

Nhờ mọi người ạ!!!!:3 

Làm em tick cho^^

Answer 1

[JOKER_Võ Văn Quốc]

Ta có \(\left(9+1\right)\left(9^2+1\right)\left(9^4+1\right)\left(9^8+1\right)\left(9^{16}+1\right)\left(9^{32}+1\right)\)

\(=\frac{1}{8}\left(9-1\right)\left(9+1\right)\left(9^2+1\right)\left(9^4+1\right)\left(9^8+1\right)\left(9^{16}+1\right)\left(9^{32}+1\right)\)

\(=\frac{1}{8}\left(9^2-1\right)\left(9^2+1\right)\left(9^4+1\right)\left(9^8+1\right)\left(9^{16}+1\right)\left(9^{32}+1\right)\)

cứ như thế

\(=\frac{1}{8}\left(9^{64}-1\right)< 9^{64}-1\)=>đpcm