So sánh:

a) \(A=\frac{n}{n+1};B=\frac{n+2}{n+3}\left(n\inℕ\right)\)

b) \(A=\frac{n}{n+3};B=\frac{n-1}{n+4}\left(n\inℕ^∗\right)\)

c) \(A=\frac{n}{2n+1};B=\frac{3n+1}{6n+3}\left(n\inℕ\right)\)

Giúp mình nhé gấp lắm ai trả lời đầu tiên mình sẽ tick

Với \(n\inℕ^∗\), cho:

\(A=1+\frac{1}{3}+...+\frac{1}{2n-3}+\frac{1}{2n-1}\)

\(B=\frac{1}{1\left(n-1\right)}+\frac{1}{3\left(2n-3\right)}+...+\frac{1}{\left(2n-3\right)\cdot3}+\frac{1}{\left(2n-1\right)\cdot1}\)

Tính \(\frac{A}{B}\).

Bài 1: CMR

a) A = \(\frac{\left(n+1\right).\left(n+2\right)....\left(2n-1\right).\left(2n\right)}{2^n}\) là số nguyên.

b) B = \(\frac{3.\left(n+1\right).\left(n +2\right)...\left(3n-1\right).3n}{3^n}\)là số nguyên.

Chứng minh rằng:

a)\(\frac{1\cdot3\cdot5\cdot\cdot\cdot39}{21\cdot22\cdot23\cdot\cdot\cdot40}=\frac{1}{2^{20}}\)

b)\(\frac{1\cdot3\cdot5\cdot\cdot\cdot\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\cdot\cdot\cdot2n}=\frac{1}{2^n}\)Với \(n\inℕ^∗\)

\(n\ge3;n\inℕ\)

CMR:

\(\frac{1}{a^n\left(b+c\right)}+\frac{1}{b^n\left(c+a\right)}+\frac{1}{c^n\left(a+b\right)}\ge\frac{3}{2}\)

17/lim\(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2n-1\right)\left(2n+1\right)}\right)\)

18/lim\(\frac{1+a+a^2+...+a^n}{1+b+b^2+...+b^n}\left(\left|a\right|< 1;\left|b\right|< 1\right)\)

19/lim\(\frac{1-2+3-4+...+\left(2n-1\right)-2n}{2n+1}\)

Cứu mình với!

a/ Cho \(\frac{a}{b}=\frac{60}{108}\)sao cho [a;b] = 180. Tìm phân số đó.

b/ Chứng minh \(\frac{1.3.5.....\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right).....\left(2n\right)}=\frac{1}{2^n}\)(n \(\in\)N^*)

Các bạn giải từng câu một cũng dc nhé