Question

hãy chứng minh:

a.a.a.a.a.a chia hết cho 7

(ab+ba) chia hết cho 11

abcabc chia hết cho 11

2 +2mũ 2+2 mũ 3+......+2 mũ 2007+2 mũ 2008

 

Answer 1

\(ab+ba=(10a+b)+(10b+a)\)

\(=10a+b+10b+a\)

\(=11a+11b\)

\(=11\left(a+b\right)\)

\(a+b\inℕ\Rightarrow ab+ba⋮11\)

Answer 2

\(A=2+2^2+2^3+\cdot\cdot\cdot+2^{2008}\)

\(\Rightarrow2A=2^2+2^3+2^4+\cdot\cdot\cdot+2^{2009}\)
\(\Rightarrow2A-A=\left(2^2+\cdot\cdot\cdot2^{2009}\right)-\left(2+\cdot\cdot\cdot+2^{2008}\right)\)

\(\Rightarrow A=2^{2009}-2\)