M=100

Xét tử N

92-(1/9)-(2/10)-(3/11)- ... -(90/98)-(91/99)-(92/100)

=(1+1+1+...+1)-(1/9)-(2/10)-(3/11)- ... -(90/98)-(91/99)-(92/100)

=1-(1/9)+1-(2/10)+1-(3/11)+......+1-(90/98)+1-(91/99)+1-(92/100)

=(8/9)+(8/10)+(8/11)+ ...+ (8/98)+(8/99)+(8/100)

=8.[(1/9)+(1/10)+(1/11)+...+(1/98)+(1/99)+(1/100)]

=40[(1/45)+(1/50)+(1/55)+...+(1/495)+(1/500)]

=>N=40

=>M/N=5/2

Bài 1:

\(A=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+1986}\right)\)

Nhận xét: \(1-\frac{1}{1+2+...+n}=1-\frac{2}{n\left(n+1\right)}=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n-1\right)\left(n+2\right)}{n\left(n+1\right)}\)

Do đó: \(\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+...+1986}\right)\)

\(=\frac{1\cdot4}{2\cdot3}\cdot\frac{2\cdot5}{3\cdot4}\cdot...\cdot\frac{1985\cdot1988}{1986\cdot1987}=\frac{1\cdot4\cdot1988}{1986\cdot3}=\frac{3976}{2979}\)

Bài 2:

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

\(\Rightarrow\frac{4\cdot4^5}{3\cdot3^5}\cdot\frac{6\cdot6^5}{2\cdot2^5}=2^x\)\(\Rightarrow\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=2^x\)

\(\Rightarrow\frac{\left(2^2\right)^6}{3^6}\cdot\frac{\left(2\cdot3\right)^6}{2^6}=2^x\)\(\Rightarrow\frac{2^{12}}{3^6}\cdot\frac{2^6\cdot3^6}{2^6}=2^x\)

\(\Rightarrow\frac{2^6\cdot3^6\cdot2^{12}}{2^6\cdot3^6}=2^x\)\(\Rightarrow2^{12}=2^x\Rightarrow x=12\)

đúng rồi đó bạn ks bạn ý đi chứ

1. ​29/15
2. 23
3. 23/12
4. 5/6
5. 5/4
6. -31/12
7. 31/6
8. -13/3
9. 1087/180
10. 1/6
11. 1/6
12. 2
13. -67/24

\(1.a)\dfrac{2^3+3.26-4^3}{2^3.3^2}\)

\(=\dfrac{2^3.3.2.13-\left(2^2\right)^3}{2^3.3^2}\)

\(=\dfrac{2^4.3.13-2^6}{2^3.3^2}\)

\(=\dfrac{2^3\left(2.3.13-2^3\right)}{2^3.3^2}\)

\(=\dfrac{78-8}{9}\)

\(=\dfrac{70}{9}\)

\(b)\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

\(=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^4.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)

\(=\dfrac{2^{12}.3^{10}+2^{13}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{2^{12}.3^{10}\left(1+2.5\right)}{2^{11}.3^{11}\left(2.3\right)}\)

\(=\dfrac{2.11}{3.6}\)

\(=\dfrac{11}{9}\)

\(2.3^{x-1}-3^{x+1}=90\)

\(\Leftrightarrow3^x:3-3^x.3=90\)

\(\Leftrightarrow3^x\left(\dfrac{1}{3}-3\right)=90\)

\(\Leftrightarrow3^x.\dfrac{-8}{3}=90\)

\(\Leftrightarrow3^x=\dfrac{-135}{4}\)

\(\Leftrightarrow\) \(x\) không có giá trị nào để thỏa mãn đề bài.

Vậy \(x\in\varnothing\)

nữ thám tử nổi tiếng

Đề bài câu 2 sai thì phải, nếu đề bài đc sửa lại là \(3^{x-1}+3^{x+1}=90\) thì \(x=3\) có lẽ là đúng

=30/12+(-4/12)+3/12

=29/12