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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(M=5+5^2+5^3+...+5^{60}\)
\(\Leftrightarrow\)\(5M=5^2+5^3+5^4+...+5^{61}\)
\(\Leftrightarrow\)\(5M-M=\left(5^2+5^3+5^4+...+5^{61}\right)-\left(5+5^2+5^3+...+5^{60}\right)\)
\(\Leftrightarrow\)\(4M=5^{61}-5\)
\(\Leftrightarrow\)\(M=\frac{5^{61}-5}{4}\)
Vậy \(M=\frac{5^{61}-5}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 5M=5(\(5+5^2++.......+5^{60}\)
5M=\(5^2+5^3+...+5^{61}\)
5M-M=\(\left(5^2+5^3+...+5^{61}\right)-\left(5+5^2+5^3+...+5^{60}\right)\)
4M=\(5^{61}-5\)
M=\(\left(5^{61}-5\right):4\)
b) \(\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{59}+5^{60}\right)\)
\(5\left(1+5\right)+5^3\left(1+5\right)+...+5^{59}\left(1+5\right)\)
\(5\cdot6+5^3\cdot6+...+5^{59}\cdot6\)
\(6\left(5+5^3+5^5+...+5^{59}\right)\)
\(\Rightarrow M⋮6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) M = 5 + 52 + 53 + .... + 560
=> 5M = 5 . 5 + 52 . 5 + 53 . 5 + ... + 560 . 5
=> 5M = 52 + 53 + 54 + .... + 561
=> 5M - M = 561 - 5
=> 4M = 561 - 5
=> M = \(\frac{\text{5^{61} - 5}}{4}\)\(\frac{5^{61}-5}{4}\)
b) M = 5 + 52 + 53 + .... + 560
=> M = ( 5 + 52 ) + ( 53 + 54 ) + .... + ( 559 + 560 )
=> M = 5 . ( 50 + 51 ) + 53 . ( 50 + 51 ) + ... + 559 . ( 50 + 51 )
=> M = 5 . 6 + 53 . 6 + ... + 559 . 6
=> M = 6 . ( 5 + 53 + ... + 559 ) \(⋮\)6 => đpcm
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có
M = 5 + 52 + 53 + ... + 5100
Mx5 = 5 x ( 5 + 52 + 53 + ... + 5100 )
Mx5 = 52 + 53 + 54 + ... + 5101
Mx5-M= ( 52 + 53 + 54 + ... + 5101 ) - ( 5 + 52 + 53 + ... + 5100 )
Mx4 = 5101 - 5
=> Mx4+5=5101
mà 4M+5=5n
=> n = 101
minh biet lam chi toi hoi day dong
kb nha xong minh giai cho
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1 :
\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)
\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)
\(\Rightarrow M< N\)
Bài 3 :
a) \(t^2+5t-8\) khi \(t=2\)
\(=5^2+2.5-8\)
\(=25+10-8\)
\(=27\)
b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)
\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)
\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)
c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)
\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)
\(\left(1\right)=1^3=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
suy ra : 5M= 5^2 +5^3 +.....+5^101
suy ra : 5M -M =5^2+5^3+...+5^101-5-5^2-
suy ra: 4M= 5^101-5
suy ra: 4M+5 = 5^101
suy ra: 5^n = 5^101
suy ra : n=101
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
M = 5 + 52 + 53 + ... + 560
=> 5M = 5.(5 + 52 + 53 + ... + 560)
=> 5M = 52 + 53 + 54 + ... + 561
=> 5M - M = (52 + 53 + 54 + ... + 561) - (5 + 52 + 53 + ... + 560)
=> 4M = 561 - 5
=> M = (561 - 5) : 4
a)Ta có :
\(M=5+5^2+5^3+...+5^{60}\)
\(5M=5^2+5^3+5^4+...+5^{61}\)
\(5M-M=\left(5^2+5^3+5^4+...+5^{61}\right)-\left(5+5^2+5^3+...+5^{60}\right)\)
\(4M=5^{61}-5\)
\(M=\frac{5^{61}-5}{4}\)