a) \(\dfrac{32}{\left(-2\right)^n}=4\)

\(\Rightarrow\left(-2\right)^n=8=\left(-2\right)^3\)

=> n = 3

b) \(\dfrac{8}{2^n}=2\)

\(\Rightarrow2^n=4=2^2\)

=> n = 2

c) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\)

=> 2n - 1 = 3

=> 2n = 4

=> n = 2

Giải:

a) \(\dfrac{32}{\left(-2\right)^n}=4\) 

\(\Rightarrow\left(-2\right)^n=32:4=8\) 

\(\Rightarrow\left(-2\right)^n=8\) 

Vì \(\left(-2\right)^n=2^3\) là ko thể nên n ∈ ∅

b) \(\dfrac{8}{2^n}=2\)

\(\Rightarrow2^n=8:2=4\) 

\(\Rightarrow2^n=4\) 

\(\Rightarrow2^n=2^2\) 

\(\Rightarrow n=2\) 

c) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\) 

\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\) 

\(\Rightarrow2n-1=3\rightarrow n=2\)

a, 59x + 46y = 2004

Vì 2004 là số chẵn, 46y là số chẵn => 59x là số chẵn

=> x là số chẵn, mà x là số nguyên tố

=> x = 2

=> 2.59 + 46y = 2004

=> 46y = 2004 ‐ 118

=> 46y = 1886

=> y = 1886:46 => y = 41

Vậy x = 2; y = 41

đã làm đề 23 rùi hả!!!!!

a: \(\left(n^2+3n-1\right)\left(n+2\right)-n^3+2\)

\(=n^3+2n^2+3n^2+6n-n-2+n^3+2\)

\(=5n^2+5n=5\left(n^2+n\right)⋮5\)

b: \(\left(6n+1\right)\left(n+5\right)-\left(3n+5\right)\left(2n-1\right)\)

\(=6n^2+30n+n+5-6n^2+3n-10n+5\)

\(=24n+10⋮2\)

d: \(=\left(n+1\right)\left(n^2+2n\right)\)

\(=n\left(n+1\right)\left(n+2\right)⋮6\)

a) Ta có: \({u_{n + 1}} - {u_n} =[2\left( {n + 1} \right) - 1] - (2n - 1) = 2\left( {n + 1} \right) - 1 - 2n + 1 = 2 > 0 \Rightarrow {u_{n + 1}} > {u_n},\;\forall \;n \in {N^*}\)

Vậy \(\left( {{u_n}} \right)\) là dãy số tăng.

b) Ta có: \({u_{n + 1}} - {u_n} = [- 3\left( {n + 1} \right) + 2] - (3n +  2) =  - 3\left( {n + 1} \right) + 2 + 3n - 2 =  - 3 < 0\;\)

Vậy \(\left( {{u_n}} \right)\) là dãy số giảm.

c, Ta có:

\(\begin{array}{l}{u_1} = \frac{{{{( - 1)}^{1 - 1}}}}{{{2^1}}} = \frac{1}{2} > 0\\{u_2} = \frac{{{{( - 1)}^{2 - 1}}}}{{{2^2}}} =  - \frac{1}{4} < 0\\{u_3} = \frac{{{{( - 1)}^{3 - 1}}}}{{{2^3}}} = \frac{1}{8} > 0\\{u_4} = \frac{{{{( - 1)}^{4 - 1}}}}{{{2^4}}} =  - \frac{1}{{16}} < 0\\...\end{array}\)

Vậy \(\left( {{u_n}} \right)\) là dãy số không tăng không giảm.

\(a=\lim4^n\left(1-\left(\dfrac{3}{4}\right)^n\right)=+\infty.1=+\infty\)

\(b=\lim\left(4^n+2.2^n+1-4^n\right)=\lim2^n\left(2+\dfrac{1}{2^n}\right)=+\infty.2=+\infty\)

\(c=limn^3\left(\sqrt{\dfrac{2}{n}-\dfrac{3}{n^4}+\dfrac{11}{n^6}}-1\right)=+\infty.\left(-1\right)=-\infty\)

\(d=\lim n\left(\sqrt{2+\dfrac{1}{n^2}}-\sqrt{3-\dfrac{1}{n^2}}\right)=+\infty\left(\sqrt{2}-\sqrt{3}\right)=-\infty\)

\(e=\lim\dfrac{3n\sqrt{n}+1}{\sqrt{n^2+3n\sqrt{n}+1}+n}=\lim\dfrac{3\sqrt{n}+\dfrac{1}{n}}{\sqrt{1+\dfrac{3}{\sqrt{n}}+\dfrac{1}{n^2}}+1}=\dfrac{+\infty}{2}=+\infty\)

\(a=\lim\dfrac{1}{\sqrt{4n+1}+2\sqrt{n}}=\dfrac{1}{\infty}=0\)

\(b=\lim n\left(\sqrt{1+\dfrac{2}{n}}-\sqrt{1-\dfrac{2}{n}}-1\right)=+\infty.\left(-1\right)=-\infty\)

\(c=\lim4^n\left(\sqrt{\left(\dfrac{9}{16}\right)^n-\left(\dfrac{3}{16}\right)^n}-1\right)=+\infty.\left(-1\right)=-\infty\)

\(d=\lim n^3\left(3+\dfrac{2}{n}+\dfrac{1}{n^2}\right)=+\infty.3=+\infty\)

\(=\lim\dfrac{\left(2+\dfrac{1}{n\sqrt{n}}\right)\left(1+\dfrac{3}{\sqrt{n}}\right)}{\left(1+\dfrac{1}{n}\right)\left(1+\dfrac{2}{n}\right)}=\dfrac{2.1}{1.1}=2\)