Question

Chung minh rang :

3ⁿ⁺²-2ⁿ⁺²+3ⁿ-2^{n chia het cho 10}

Answer 1

Ta có:

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

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

\(=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\)

\(=3^n.10-2^n.5\)

Vì \(\left\{{}\begin{matrix}3^n.10⋮10\\2^n.5⋮10\end{matrix}\right.\)

Nên \(3^{n+2}-2^{n+2}+3^n-2^n\) chia hết cho 10

Answer 2

Cho gửi nhờ đề

Answer 3

Cho a,b,c>0 thỏa mãn \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{8}\)

Chứng minh rằng: \(\frac{1}{2a+b+c}+\frac{1}{a+2b+c}+\frac{1}{a+b+2c}\le2\)