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a) \(M=1+3+3^2+3^3+...+3^{119}\)
\(3M=3+3^2+3^3+3^4+...+3^{119}+3^{120}\)
\(3M-M=\left(3+3^2+3^3+...+3^{120}\right)-\left(1+3+3^2+...+3^{119}\right)\)
\(2M=3^{120}-1\)
\(M=\frac{3^{120}-1}{2}\)
b) \(M=1+3+3^2+3^3+...+3^{118}+3^{119}\)
\(=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+...+\left(3^{117}+3^{118}+3^{119}\right)\)
\(=\left(1+3+3^2\right)+3^3\left(1+3+3^2\right)+...+3^{117}\left(1+3+3^2\right)\)
\(=13\left(1+3^3+...+3^{117}\right)\)chia hết cho \(13\).
\(M=1+3+3^2+3^3+...+3^{118}+3^{119}\)
\(=\left(1+3+3^2+3^3\right)+...+\left(3^{116}+3^{117}+3^{118}+3^{119}\right)\)
\(=\left(1+3+3^2+3^3\right)+...+3^{116}\left(1+3+3^2+3^3\right)\)
\(=40\left(1+3^4+...+3^{116}\right)\)chia hết cho \(5\).
a) A= (\(2^9.3+2^9.5\)) : \(2^{12}\)
= \(2^9\)(3+5) : \(2^{12}\)
= \(2^9.8:2^{12}\)
= \(2^9.2^3:2^{12}\)
= \(2^{12}:2^{12}\)
=1
a)3 . 103 + 2 . 102 + 5 . 10
= 3 . 102 . 10 + 2 . 10 . 10 + 5 . 10
= 10 . ( 3 . 102 + 2 . 10 + 5 )
= 10 . ( 3 . 100 + 20 + 5 )
= 10 . ( 300 + 20 + 5 )
= 10 . 325
= 3250
a) 3 . 103 + 2 . 102 + 5 . 10
= 3 . 1000 + 2 . 100 + 5 . 10
= 3000 + 200 + 50
= 3250
a)[(33 - 3) : 3]3 + 3
= ( 30 : 3 )6
= 106
b)25 + 2 . {12 + 2 .[3 . (5 - 2) + 1} + 1
= 32 + 2 . [12 + 2 . ( 3 . 3 + 1 )] + 1
= 32 + 2 . [ 12 + 2 . ( 9 + 1 )] + 1
= 32 + 2 . ( 12 + 2 . 10 ) + 1
= 32 + 2 . ( 12 + 20 ) + 1
= 32 + 2 . 32 + 1
= 32 . ( 1 + 2 ) + 1
= 32 . 3 = 96 + 1 = 97