ĐGNL ĐHQG Hà Nội - Tư duy định lượng - Giới hạn của dãy số

A.\[{u_n} = \frac{n}{2}\]

B. \[{u_n} = \frac{2}{n}\]

C. \[{u_n} = n\]

D. \[{u_n} = \sqrt n \]

A.\[\lim \frac{{3{u_n} - 1}}{{{u_n} + 1}} = 3\]

B. \[\lim \frac{{3{u_n} - 1}}{{{u_n} + 1}} = - 1\]

C. \[\lim \frac{{3{u_n} - 1}}{{{u_n} + 1}} = 2\]

D. \[\lim \frac{{3{u_n} - 1}}{{{u_n} + 1}} = 1\]

A.\[{u_n} = \frac{1}{{\sqrt n }}\]

B. \[{u_n} = \frac{1}{{\sqrt[3]{n}}}\]

C. \[{u_n} = \frac{{\sqrt[3]{n}}}{2}\]

D. \[{u_n} = 0\]

A.\[\lim {u_n} = 0\]

B. \[\lim {u_n} >\lim {v_n}\]

C. \[\lim {u_n} < \lim {v_n}\]

D. \[\lim {u_n} < 0\]

A.\[\lim {q^n} = 0\]

B. \[\lim q = 0\]

C. \[\lim \left( {n.q} \right) = 0\]

D. \[\lim \frac{n}{q} = 0\]

A.\[\mathop {\lim }\limits_{n \to + \infty } \left( {{u_n} - L} \right) = 0\]

B. \[\mathop {\lim }\limits_{n \to + \infty } \left( {{u_n}} \right) = 0\]

C. \[\mathop {\lim }\limits_{n \to + \infty } L = 0\]

D. \[\mathop {\lim }\limits_{n \to + \infty } \left( {{u_n} + L} \right) = 0\]

A.\[\lim \left| {{u_n}} \right| = L\]

B. \[\lim \left| {{u_n}} \right| = - L\]

C. \[\lim {u_n} = \left| L \right|\]

D. \[\lim \left| {{u_n}} \right| = \left| L \right|\]

A.\[\lim \sqrt[3]{{{u_n}}} = L\]

B. \[\lim \sqrt {{u_n}} = L\]

C. \[\lim \sqrt {{u_n}} = \sqrt L \]

D. \[\lim \sqrt[3]{{{u_n}}} = \sqrt[3]{L}\]

A.\[\lim \left( {{u_n} + {v_n}} \right) = L + M\]

B. \[\lim \left( {{u_n} + {v_n}} \right) = L - M\]

C. \[\lim \left( {{u_n} - {v_n}} \right) = L + M\]

D. \[\lim \left( {{u_n} - {v_n}} \right) = L.M\]

A.\[\lim \left( {{u_n} - {v_n}} \right) = L - M\]

B. \[\lim \left( {{u_n} + {v_n}} \right) = L + M\]

C. \[\lim \left( {{u_n}.{v_n}} \right) = L.M\]

D. \[\lim \left( {c{u_n}} \right) = cM\]

A.\[S = \frac{{{u_1}}}{{1 - q}}\]

B. \[S = \frac{{{u_1}}}{{q - 1}}\]

C. \[S = \frac{{1 - q}}{{{u_n}}}\]

D. \[S = \frac{{{u_1}}}{{1 - {q^n}}}\]

A.\[\lim n = + \infty \]

B. \[\lim \sqrt n = + \infty \]

C. \[\lim \sqrt[3]{n} = + \infty \]

D. \[\lim \frac{1}{n} = + \infty \]

A.\[\lim \left( {{u_n}.{v_n}} \right) = 0\]

B. \[\lim \left( {{u_n}.{v_n}} \right) = + \infty \]

C. \[\lim \left( {{u_n}.{v_n}} \right) = - \infty \]

D. \[\lim \left( {{u_n}.{v_n}} \right) = 1\]

A.\[\lim {(\sqrt 2 )^n} = 0\]

B. \[\lim {\left( {\frac{1}{3}} \right)^n} = 0\]

C. \[\lim {\left( {\frac{1}{{\sqrt 2 }}} \right)^n} = 0\]

D. \[\lim {\left( {\frac{1}{{\sqrt 3 }}} \right)^n} = 0\]

A.\[S = \frac{{{u_1}}}{{1 - q}}\]

B. \[S = \frac{{{u_1}}}{{1 + q}}\]

C. \[S = \frac{1}{{{u_1} - q}}\]

D. \[S = \frac{{{u_1}}}{{q - 1}}\]

A.\[\frac{1}{5}.\]

B. \[ - \frac{4}{5}.\]

C. \[\frac{4}{5}.\]

D. \[ - \frac{1}{5}.\]

A.\(0\)

B. \[ - \frac{1}{4}.\]

C. \[\frac{3}{4}.\]

D. \[ - \frac{3}{4}.\]

A..0.    

B.\[ - \frac{1}{4}.\]

C. \[\frac{3}{4}.\]

D. \[ - \frac{3}{4}.\]

A.0.     

B.1.    

C.\[\frac{3}{5}.\]

D. \[ + \infty .\]

A.\[\lim \frac{{2{n^2} - 3}}{{ - 2{n^3} - 4}}.\]

B. \[\lim \frac{{2{n^2} - 3}}{{ - 2{n^2} - 1}}.\]

C. \[\lim \frac{{2{n^2} - 3}}{{2{n^2} + 1}}.\]

D. \[\lim \frac{{2{n^3} - 3}}{{2{n^2} - 1}}.\]

A.0

B.1

C.\[ - \infty \]

D. \[ + \infty \]

A.1.    

B.\[\frac{2}{3}.\]

C. -1

D. \[ - \frac{1}{3}.\]

A.−4.

B.−1.

C.5.    

D.\[ - \frac{3}{2}.\]

A.\[\frac{5}{2}.\]

B. \[\frac{{ - 5}}{2}.\]

C. 1

D. -1

A.1.

B.\(\sqrt 2 \)

C. 2

D. \[\frac{1}{{\sqrt 2 }}.\]

A.\[ - \infty .\]

B. \( - \frac{1}{2}\)

C. 0

D. \[ + \infty .\]

A..0.

B.\( - \frac{1}{2}\)

C. \[ - \frac{1}{{\sqrt 2 }}.\]

D. \[\frac{1}{{\sqrt 2 }}.\]

A.0.    

B.\(\frac{1}{2}\)

C. 1

D. 2

A.\(\frac{1}{2}\)

B. \[\frac{1}{4}.\]

C. 1

D. 2

A.0.

B.1.

C.\[ + \infty .\]

D. 2

A.\[ - \infty .\]

B. -1

C. \[ + \infty .\]

D. \[\frac{{ - 2}}{5}.\]

A.Dãy \[\left( {{u_n}} \right)\]là dãy giảm tới 1 khi \[n \to + \infty \]

B.Dãy \[\left( {{u_n}} \right)\]là dãy tăng tới 1 khi \[n \to + \infty \]

C.Không tồn tại giới hạn của dãy \[\left( {{u_n}} \right)\]

D.Cả 3 đáp án trên đều sai

A.\[ + \infty \]

B. \[\frac{{1 - a}}{{1 - b}}\]

C. \[\frac{{1 - b}}{{1 - a}}\]

D. 1

A.\[ + \infty .\]

B. 0

C. \(\frac{1}{2}\)

D. 1

A.\[ + \infty \]

B. \[ - \infty \]

C. 0

D. 1

A.1

B.0

C.\[ + \infty \]

D. \(\frac{1}{2}\)

A.\[\frac{1}{5}\]

B. \(\frac{1}{2}\)

C. 0

D. \[\frac{{ - 3}}{2}\]

A.0

B.\[ - \infty \]

C. \(\frac{1}{2}\)

D. \[ - \frac{1}{3}\]

A.9a

B.6a

C.\[ + \infty \]

D.3a

A.\[\mathop {\lim }\limits_{n \to - \infty } {u_n} = - \infty \]

B. \[\mathop {\lim }\limits_{n \to + \infty } {u_n} = - \infty \]

C. \[\mathop {\lim }\limits_{n \to - \infty } {u_n} = + \infty \]

D. \[\mathop {\lim }\limits_{n \to + \infty } {u_n} = + \infty \]

A.\[S = 1\]

B. \[S = \frac{1}{{{2^n}}}\]

C. \[S = 0\]

D. \[S = 2\]

A.\[\frac{{{a^2}\left( {{2^{100}} - 1} \right)}}{{{2^{100}}}}\]

B. \[2{a^2}\]

C. \[\frac{{{a^2}}}{{{2^{100}}}}\]

D. \[\frac{{{a^2}\left( {{2^{99}} - 1} \right)}}{{{2^{98}}}}\]