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Để A>0 thì \(\dfrac{1}{x-1}>0\)
=>x>1
mà x<4
nên 1<x<4
mà x nguyên
nên x=2 hoặc x=3
![](https://rs.olm.vn/images/avt/0.png?1311)
6\(^2\)+ 64 : ( x - 1 ) = 52
36 + 64 : ( x - 1 ) =52
64 ; ( x - 1 ) =64 : 52
x - 1 = \(\frac{16}{13}\)
x = \(\frac{16}{13}\)+1
x = \(\frac{29}{13}\)
HT
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Goi tong tren la A
A = 1 + 1/2.2 + 1/3.3 +......+ 1/100.100
A < 1 + 1/1.2 + 1/2.3 + 1/3.4 +.......+ 1/99.100
A < 1 + 1 - 1/2 + 1/2 - 1/3 +.....+ 1/99 - 1/100
A < 2 - 1/2 - 1/100
A < 2 - 49/100 < 2
=> A < 2 (dpcm)
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`1/15+1/35+1/63+1/99+1/143`
`=1/[3.5]+1/[5.7]+1/[7.9]+1/[9.11]+1/[11.13]`
`=1/2(2/[3.5]+2/[5.7]+2/[7.9]+2/[9.11]+2/[11.13])`
`=1/2.(1/3-1/5+1/5-1/7+...+1/11-1/13)`
`=1/2.(1/3-1/13)`
`=1/2 . 10/39`
`=5/39`
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Nếu đề là tìm n để phím chia hết thì làm như sau
n^2 +3n -7 : n-3
n(n+3)-7: n-3
vì n(n+3) chia hết cho n+3 nên để n^2 +3n -7 chia hết cho n+3 thì -7 chia hết cho n+3
=> n+3 thuộc Ư(7)={1,7,-1,-7}
n+3=1 => n= -2
n+3=7 => n= 4
n+3 = -1 => n=-4
n+3=7 => n =-10
b, n^2 +5 : n+1
n^2 -1+6 : n+1
(n-1)(n+1) + 6: n+1 ( n^2 -1 =(n+1)(n-1) là dùng hằng đẳng thức lớp 8 sẽ học)
vì (n-1)(n+1) chia hết cho n+1 nên để n^2 +5 chia hết n+1 thì 6 phải chia hết cho n+1
=> n+1 thuộc Ư(6)={1,2,3,6,-1,-2,-3,-6}
n+1 =1 =>n=0
n+1=2=>n=1
n+1=3=>n=2
n+1=6=>n=5
n+1=-1=>n=-2
n+1=-2=>n=-3
n+1=-3=>n=-4
n+1=-6=>n=-7
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(A=\frac{1}{3}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{195}\)
\(\Rightarrow2A=\frac{2}{3}+\frac{2}{15}+\frac{2}{21}+...+\frac{2}{195}\)
\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{1}-\frac{1}{15}\)
\(=\frac{14}{15}\)
\(\Rightarrow2A=\frac{14}{15}\Rightarrow A=\frac{14}{15}\div2=\frac{7}{15}\)
Vậy A = 7/15
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Đặt \(A=1+2+2^2+2^3+...+2^{64}\)
\(\Rightarrow2A=2+2^2+2^3+...+2^{65}\)
\(\Rightarrow2A-A=2+2^2+2^3+...+2^{65}-\left(1+2+2^2+...+2^{64}\right)\)
\(\Rightarrow A=2+2^2+2^3+...+2^{65}-1-2-2^2-...-2^{64}\)
\(\Rightarrow A=2^{65}-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) S=1 + 2 + 2^2 + 2^3 +...+ 2^63
2S=2 + 2^2 + 2^3 + 2^4 +...+ 2^64
S=2S-S=(2 + 2^2 + 2^3 + 6^4 +...+ 2^64)-(1 + 2 + 2^2 + 2^3 +...+ 2^63)
S=2 + 2^2 + 2^3 + 2^4 +...+ 2^64 - 1 - 2 - 2^2 - 2^3 -...- 2^63
S=2^64 - 1