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7x + 135 : 45=52
7x + 3 = 52
7x= 52 - 3
7x= 49
7x= \(7^2\)
\(\Rightarrow\) x=2
{23 - [15-(27 - 25)2] : (32 . 77 - 22 . 13)} : (3 + 8)1
= {23 - [15- 22 ] : (9 . 77 -4 . 13} : 11
= {23 - [15 - 4 ] : ( 693 - 52 ) } :11
= {23 - 11 : 17 } :11
= { 23 - \(\frac{11}{17}\) } : 11
= \(\frac{380}{17}\) : 11
= \(\frac{380}{187}\)
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 \(5\).