chứng tỏ rằng A=2+2mu 2+2mu 3 +...+2mu 9+ 2mu 10 chia hết cho 3 và 31
cho a= 2mu 2+ 2 mu 3+2mu4+....+2mu 12
chung to rang a chia hết cho 39
bai1 12mu n+1 + 11mu n+2 chia hết cho 133
bai2 3mu n+2 -2mu n+2 + 3 mu n -2mu n
F= 1+2+2mu 2+.....+2mu 9
2mu a + 2mu b + 2mu c =10368 tim a,b,c
A = 2mu 0 + 2 mu 1 + 2mu 2 + ...+ 2 mu 50
A= \(2^0+2^1+2^2+...+2^{50}\)
\(\Rightarrow\)2A =2(\(2^0+2^1+2^2+...+2^{50}\))
\(\Rightarrow\)2A= \(2+2^2+2^3+2^4+...+2^{51}\)
\(\Rightarrow\)2A-A= (\(2+2^2+2^3+2^4+...+2^{51}\))-(\(2+2^2+2^3+2^4+...+2^{50}\))
\(\Rightarrow\)A= \(2^{51}-1\)
A = 2mu 0 + 2 mu 1 + 2mu 2 + ...+ 2 mu 50
(5 mu 4 + 4 mu 7) (8 mu9 - 2mu 7) (2mu 4-4 mu 2)
2mu x +15 = 31
X=???
\(2^x+15=31\\ 2^x=31-15\\ 2^x=16=2^4\\ x=4\)
\(2^x+15=31\)
\(2^x=31-15\)
\(2^x=16\)
\(2^x=2^4\)
\(\Rightarrow x=4\)
2mu n +2 mu n+3 =144
\(2^n+2^{n+3}=144\)
\(\Rightarrow2^n+2^n\cdot8=144\)
\(\Rightarrow2^n\cdot\left(1+8\right)=144\)
\(\Rightarrow2^n\cdot9=144\)
\(\Rightarrow2^n=144:9=16\)
\(\Rightarrow2^n=2^4\)
\(\Rightarrow n=4\)
\(2^n+2^{n+3}=144\)
\(2^n+2^n.2^3=144\)
\(2^n.\left(1+2^3\right)=144\)
\(2^n.9=144\)
\(2^n=144:9=16\)
ta có \(16=2^4\)
nên \(n=4\)