Cho:

\(A=\dfrac{1}{1.\left(2n-1\right)}+\dfrac{1}{3.\left(2n-3\right)}+...+\dfrac{1}{\left(2n-3\right).3}+\dfrac{1}{\left(2n-1\right).1}\) \(B=1+\dfrac{1}{3}+...+\dfrac{1}{2n-1}\) (với n ∈ N*).

Tính \(\dfrac{A}{B}\)

Cho A = \(\dfrac{1}{1.\left(2n-1\right)}+\dfrac{1}{3.\left(2n-3\right)}+...+\dfrac{1}{3.\left(2n-3\right)}+\dfrac{1}{1.\left(2n-1\right)}\); B = \(1+\dfrac{1}{3}+...+\dfrac{1}{2n-1}\). Tính \(\dfrac{A}{B}\)

Tìm n?

\(3C^o_{2n}-\dfrac{1}{2}C^1_{2n}-\dfrac{1}{4}C^3_{2n}+...+\dfrac{3}{2n+1}C^{2n}_{2n}=\dfrac{10923}{5}\)

cho

A=\(\dfrac{1}{1\left(2n-1\right)}+\dfrac{1}{3\left(2n-3\right)}+...+\dfrac{1}{\left(2n-3\right)3}+\dfrac{1}{\left(2n-1\right)1}\)

B=\(1+\dfrac{1}{3}+...+\dfrac{1}{2n-1}\)

tính \(\dfrac{A}{B}\)

Tính tổng: a) \(S=2C^2_{2n}+4C^4_{2n}+6C^6_{2n}+...+2nC^{2n}_{2n}\)

                 b) \(S=\dfrac{1}{2}C^0_{2n}+\dfrac{1}{4}C^2_{2n}+\dfrac{1}{6}C^4_{2n}+...+\dfrac{1}{2n+2}C^{2n}_{2n}\)

Tìm các giới hạn sau:

\(a,lim\dfrac{2n^2+1}{3n^3-3n+3}\)

\(b,lim\dfrac{-3n^3+1}{2n+5}\)

\(c,lim\dfrac{n^3-2n+1}{-3n-4}\)

Tìm các giới hạn sau:

a) \(lim\sqrt[3]{-n^3+2n^2-5}\)

b) \(lim\dfrac{1}{\sqrt{n+1}-\sqrt{n}}\)

c) \(lim\left(\dfrac{1}{n+1}-n\right)\)

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

e) \(lim\dfrac{2n^3+n^2-3n+1}{2-3n}\)

Tìm các giới hạn sau:

\(a,lim\dfrac{2n+1}{-3n+2}\)

\(b,lim\dfrac{5n^3-2n+1}{n-2n^3}\)

Tìm n ϵ Z sao cho n là số nguyên

\(\dfrac{2n-1}{n-1};\dfrac{3n+5}{n+1};\dfrac{4n-2}{n+3};\dfrac{6n-4}{3n+4};\dfrac{n+3}{2n-1};\dfrac{6n-4}{3n-2};\dfrac{2n+3}{3n-1};\dfrac{4n+3}{3n+2}\)

Tính :6/ lim\(\dfrac{-n^2+2n+1}{\sqrt{3n^4+2}}\)

7/ lim \(\dfrac{\sqrt{n^3-2n+5}}{3+5n}\)

10/ lim\(\dfrac{1+3+5+...+\left(2n+1\right)}{3n^3+4}\)