Question

[Phúc Anh Quân]

-So sánh các cặp số sau :

a) C= \(3^{n+1}+4.2^{n-1}-81.3^{n-3}-8.2^{n-2}+1\) Và D=\(\left(2^n+1\right)^2+\left(2^n-1\right)^2-2.\left(4^n+1\right)\) (N ∈ nguyên dương )

Answer 1

[Hoàng Lê Bảo Ngọc]

Xét \(C=3^{n+1}+4.2^{n-1}-81.3^{n-3}-8.2^{n-2}+1\)

\(=3^{n+1}+2^2.2^{n-1}-3^4.3^{n-3}-2^3.2^{n-2}+1\)

\(=3^{n+1}+2^{n+1}-3^{n+1}-2^{n+1}+1=1\)

Xét \(D=\left(2^n+1\right)^2+\left(2^n-1\right)^2-2\left(4^n+1\right)=2^{2n}+2.2^n+1+2^{2n}-2.2^n+1-2.4^n-2\)

\(=4^n+4^n-2.4^n=2.4^n-2.4^n=0\)

Vậy C > D

Answer 2

[Phúc Anh Quân]

bạn nói dùm mình chỗ từ =\(3^{n+1}+2^2.2^{n-1}-3^4.3^{n-3}-2^3.2^{n-2}+1\) 

                                      =\(3^{n+1}+2^{n+1}-3^{n+1}-2^{n+1}+1=1\)