a)Đặt \(A=7^6+7^5-7^4\)
\(A=7^4\left(7^2+7-1\right)\)
\(A=7^4\cdot55⋮55\left(đpcm\right)\)
b)\(A=1+5+5^2+5^3+...+5^{50}\)
\(5A=5+5^2+5^3+5^4+...+5^{51}\)
\(5A-A=\left(5+5^2+5^3+5^4+...+5^{51}\right)-\left(1+5+5^2+5^3+...+5^{50}\right)\)
\(4A=5^{51}-1\)
\(A=\frac{5^{51}-1}{4}\)
a)
Ta có :
\(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4.55\)
=> Chia hết cho 5
b)
Ta có :
\(A=1+5+5^2+....+5^{50}\)
\(5A=5+5^2+....+5^{51}\)
=> 5A - A = \(\left(5+5^2+....+5^{51}\right)\)\(-\left(1+5+....+5^{50}\right)\)
\(\Rightarrow4A=5^{51}-1\)
\(\Rightarrow A=\frac{5^{51}-1}{4}\)
a) Ta có: \(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.55⋮55\)
\(\Rightarrow7^6+7^5-7^4⋮55\left(đpcm\right)\)
b) Ta có: \(A=1+5+5^2+...+5^{50}\)
\(\Rightarrow5A=5+5^2+5^3+...+5^{51}\)
\(\Rightarrow5A-A=\left(5+5^2+5^3+...+5^{51}\right)-\left(1+5+5^2+...+5^{50}\right)\)
\(\Rightarrow4A=5^{51}-1\)
\(\Rightarrow A=\frac{5^{51}-1}{4}\)
Vậy \(A=\frac{5^{51}-1}{4}\)
