Ta có : D = \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+.....+\frac{4}{2008.2010}\)
\(\Leftrightarrow D=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2008.2010}\right)\)
\(\Leftrightarrow D=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(\Leftrightarrow D=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(\Leftrightarrow D=1-\frac{1}{1005}=\frac{1004}{1005}\)
D = 2.(2/2.4+2/4.6+...+2/2008.2010)
=2(1/2-1/4+1/4-1/6+......+1/2008-1/2
=2(1/2-1/2010)
=2.502/1005
=1004/1005
A=3n+1/n-1=3(n-1)+4/n-1=3+4/n-1
Để A là số nguyên thì 4/n-1 là số nguyên
=>n-1 thuộc Ư(4)=1,-1,2,-2,4,-4
=>n thuộc (2,0,3,-1,5,-3)
It very easy!!!
a) \(D=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)=2.\frac{502}{1005}=\frac{1004}{1005}\)
b) Ta có: \(A=\frac{3n+2}{n-1}\) . Để A là số nguyên thì: (3n + 2) phải chia hết cho n - 1
\(\Rightarrow3n:n=2:1=2\)
\(\Rightarrow n-1\inƯ\left(2\right)\)
Ư(2) = { 2 ; -2 ; 1 ; -1 }
Ta có bảng sau:
n - 1 | 2 | -2 | 1 | -1 |
n | 3 | -1 | 2 | 0 |
Vậy ....
Sửa lại chỗ cái bảng chút nhé:
n - 1 | 2 | -2 | 1 | -1 |
n | 3 (C) | -1 (L) | 2 (C) | 0 (C) |
Vậy n = { 3 ; 2 ; 0 }