(1) Để \(\dfrac{2n}{n-2}\) là số nguyên thì 2n⋮n-2

2n-4+4⋮n-2

2n-4⋮n-2⇒4⋮n-2

n-2∈Ư(4)⇒Ư(4)={1;-1;2;-2;4;-4}

n∈{3;1;4;0;6;-2}

(2) \(\dfrac{3}{10.12}+\dfrac{3}{12.14}+...+\dfrac{3}{48.50}\)

=\(\dfrac{3}{2}.\left(\dfrac{2}{10.12}+\dfrac{2}{12.14}+...+\dfrac{2}{48.50}\right)\)

=\(\dfrac{3}{2}.\left(\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{14}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\)

=\(\dfrac{3}{2}.\left(\dfrac{1}{10}-\dfrac{1}{50}\right)\)

=\(\dfrac{3}{2}.\dfrac{2}{25}\)

=\(\dfrac{3}{25}\)

Giải:

(1) Để \(\dfrac{2n}{n-2}\) là số nguyên thì \(2n⋮n-2\) 

\(2n⋮n-2\) 

\(\Rightarrow2n-4+4⋮n-2\) 

\(\Rightarrow4⋮n-2\) 

\(\Rightarrow n-2\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\) 

Vậy \(n\in\left\{0;1;3;4;6\right\}\)

(2) \(\dfrac{3}{10.12}+\dfrac{3}{12.14}+\dfrac{3}{14.16}+...+\dfrac{3}{48.50}\) 

\(=\dfrac{3}{2}.\left(\dfrac{2}{10.12}+\dfrac{2}{12.14}+\dfrac{2}{14.16}+...+\dfrac{2}{48.50}\right)\) 

\(=\dfrac{3}{2}.\left(\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{16}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\) 

\(=\dfrac{3}{2}.\left(\dfrac{1}{10}-\dfrac{1}{50}\right)\) 

\(=\dfrac{3}{2}.\dfrac{2}{25}\) 

\(=\dfrac{3}{25}\) 

Chúc bạn học tốt!

(1) Để biểu thức \(\dfrac{2n}{n-2}\) nguyên thì \(2n⋮n-2\)

\(\Leftrightarrow4⋮n-2\)

\(\Leftrightarrow n-2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{3;1;4;0;6;-2\right\}\)

a) A = 3/10.12 + 3/12.14 + ... + 3/998.1000

2/3.A = 2/10.12 + 2/12.14 + ... + 2/998.1000

2/3.A = 1/10 - 1/12 + 1/12 - 1/14 + ... + 1/998 - 1/1000

2/3.A = 1/10 - 1/1000

2/3.A = 99/1000

A = 99/1000 : 2/3

A = 99/1000 . 3/2

A = 297/2000

b) B = 2/1.4 + 2/4.7 + 2/7.10 + ... + 2/22.25

3/2.B = 3/1.4 + 3/4.7 + 3/7.10 + ... + 3/22.25

3/2.B = 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/22 - 1/25

3/2.B = 1 - 1/25

3/2.B = 24/25

B = 24/25 : 3/2

B = 24/25 . 2/3

B = 16/25

Ủng hộ mk nha ^_-

a) Ta có: \(A=\frac{3}{10.12}+\frac{3}{12.14}+....+\frac{3}{998.1000}.\)

 \(\Rightarrow\frac{2}{3}A=\frac{1}{10.12}+\frac{1}{12.14}+...+\frac{1}{998.1000}\)

 \(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{998}-\frac{1}{1000}\)

 \(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{1000}=\frac{99}{1000}\)

 \(\Rightarrow A=\frac{99}{1000}:\frac{2}{3}=\frac{297}{2000}\)

Ta có: \(B=\frac{2}{1.4}+\frac{2}{4.7}+...+\frac{2}{22.25}\)

\(\Rightarrow\frac{3}{2}B=\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{22.25}\)

\(\Rightarrow\frac{3}{2}B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{25}\)

\(\Rightarrow\frac{3}{2}B=1-\frac{1}{25}=\frac{24}{25}\)

\(\Rightarrow B=\frac{24}{25}:\frac{3}{2}=\frac{16}{25}\)

2/5 . A = 2/10.12 + 2/12.14 + ....... + 2/998.1000

           = 1/10 - 1/12 + 1/12 - 1/14 + ..... + 1/998 - 1/1000

           = 1/10 - 1/1000 = 99/1000

=> A = 99/1000 : 2/5 = 99/400

Tk mk nha

Mình làm tắt cũng dc nhé có gì ko dc hỏi mình nhé

Ta có:A=(5/10-5/12):2+(5/12-2/14):2+...+(5/998-5/1000):2

suy ra A=5/10-5/1000=99/200

b: 6B=2*4*6+4*6*6+6*8*6+...+46*48*6+48*50*6

=2*4*6-2*4*6+4*6*8-4*6*8+...-44*46*48+46*48*50-46*48*50+48*50*52

=48*50*52

=>B=20800

d: 9D=1*4*9+4*7*9+...+46*49*9

=1*4*2+1*4*7-1*4*7+1*7*10-1*7*10+...+46*49*52-46*49*43

=1*2*4+46*49*52

=117216

=>D=13024

a: 

bn lấy 1/2 nhân ra ngoài ròi tính như bình thường nha!

Đặt tổng trên là A ta có

\(2A=\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{48.52}\)

\(2A=\frac{12-10}{10.12}+\frac{14-12}{12.14}+\frac{16-14}{14.16}+...+\frac{50-48}{48.50}\)

\(2A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+...+\frac{1}{48}-\frac{1}{50}=\frac{1}{10}-\frac{1}{50}=\frac{2}{25}\)

\(\Rightarrow A=\frac{2A}{2}=\frac{1}{25}\)
 

\(\frac{1}{10.12}+\frac{1}{12.14}+\frac{1}{14.16}+...+\frac{1}{48.50}\)

=\(\frac{1}{5.2.2.6}+\frac{1}{6.2.2.7}+\frac{1}{7.2.2.8}+...+\frac{1}{24.2.2.25}\)

=\(\frac{1}{2}.\left(\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{24.25}\right)\)

=\(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\right)\)

=\(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{25}\right)\)

=\(\frac{1}{2}.\frac{4}{25}\)

=\(\frac{2}{25}\)

mình không biết đúng hông có gì sai cho mình xin lỗi

D = 2 3 − 1 2 . 1 4 = 1 24 E = 2 3 − 1 2 . 1 4 =  13 24 F = 3 4 − 1 − 2 . 4 6 − 1 3 = 5 12

Đặt \(A=\frac{3}{10.12}+\frac{3}{12.14}+.....+\frac{3}{48.50}\)

      \(A=\frac{3}{2}.\left(\frac{2}{10.12}+\frac{2}{12.14}+......+\frac{2}{48.50}\right)\)

      \(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{12}+....+\frac{1}{48}-\frac{1}{50}\right)\)

       \(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{50}\right)\)

      \(A=\frac{3}{2}.\frac{2}{25}\) 

     \(A=\frac{3}{25}\)

cảm ơn bạn nhiều nhé !
 

   3/10.12+3/12.14+............+3/48.50

=3/2.(2/10.12+2/12.14+..........+2/48.50)

=3/2(2/10-2/12+2/12-2/14+......+2/48-2/50)

=3/2.(2/10-2/50)

=3/2.4/25

=6/25