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