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(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 \(2n⋮n-2\)
\(2n⋮n-2\)
\(\Rightarrow2n-4+4⋮n-2\)
\(\Rightarrow4⋮n-2\)
\(\Rightarrow n-2\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)
| n-2 | -4 | -2 | -1 | 1 | 2 | 4 |
| n | -2 | 0 | 1 | 3 | 4 | 6 |
| Kết luận | loại | t/m | t/m | t/m | t/m | t/m |
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!
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: \(A=\frac{3}{10.12}+\frac{3}{12.14}+....+\frac{3}{998.1000}.\)
\(\Rightarrow\frac{2}{3}A=\frac{1}{10.12}+\frac{1}{12.14}+...+\frac{1}{998.1000}\)
\(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{998}-\frac{1}{1000}\)
\(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{1000}=\frac{99}{1000}\)
\(\Rightarrow A=\frac{99}{1000}:\frac{2}{3}=\frac{297}{2000}\)
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
Đặt tổng trên là A ta có
\(2A=\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{48.52}\)
\(2A=\frac{12-10}{10.12}+\frac{14-12}{12.14}+\frac{16-14}{14.16}+...+\frac{50-48}{48.50}\)
\(2A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+...+\frac{1}{48}-\frac{1}{50}=\frac{1}{10}-\frac{1}{50}=\frac{2}{25}\)
\(\Rightarrow A=\frac{2A}{2}=\frac{1}{25}\)
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 \(A=\frac{3}{10.12}+\frac{3}{12.14}+.....+\frac{3}{48.50}\)
\(A=\frac{3}{2}.\left(\frac{2}{10.12}+\frac{2}{12.14}+......+\frac{2}{48.50}\right)\)
\(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{12}+....+\frac{1}{48}-\frac{1}{50}\right)\)
\(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{50}\right)\)
\(A=\frac{3}{2}.\frac{2}{25}\)
\(A=\frac{3}{25}\)
S = \(\dfrac{1}{10.12}\) + \(\dfrac{1}{12.14}\) + .....+ \(\dfrac{1}{998.1000}\)
S = \(\dfrac{1}{2}\).( \(\dfrac{2}{10.12}\) + \(\dfrac{2}{12.14}\)+.....+ \(\dfrac{2}{998.1000}\))
S = \(\dfrac{1}{2}\).( \(\dfrac{1}{10}\)- \(\dfrac{1}{12}\)+ \(\dfrac{1}{12}\) - \(\dfrac{1}{14}\)+...+\(\dfrac{1}{998}\)- \(\dfrac{1}{1000}\))
S = \(\dfrac{1}{2}\). ( \(\dfrac{1}{10}\) - \(\dfrac{1}{1000}\))
S = \(\dfrac{1}{2}\).\(\dfrac{99}{1000}\)
S = \(\dfrac{99}{2000}\)