Bài 8
a)Để A là số nguyên thì n-5⋮n+1
n+1-6⋮n+1
n+1⋮n+1⇒6⋮n+1
n+1∈Ư(6)
Ư(6)={1;-1;2;-2;3;-3;6;-6}
Vậy n ∈ {0;-2;1;-3;2;-4;5;-7}
Bài 6:
1) Ta có: \(\dfrac{6}{15\cdot18}+\dfrac{6}{18\cdot21}+...+\dfrac{6}{87\cdot90}\)
\(=2\left(\dfrac{3}{15\cdot18}+\dfrac{3}{18\cdot21}+...+\dfrac{3}{87\cdot90}\right)\)
\(=2\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
\(=2\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)
\(=2\cdot\dfrac{1}{18}=\dfrac{1}{9}\)
2) Ta có: \(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{399}\)
\(=\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{19\cdot21}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{19}-\dfrac{1}{21}\)
\(=\dfrac{1}{3}-\dfrac{1}{21}\)
\(=\dfrac{7}{21}-\dfrac{1}{21}=\dfrac{6}{21}=\dfrac{2}{7}\)
Bài 6
a)Đặt A =6/15.18+6/18.21+...+6/87.90
A=2.(3/15.18+3/18.21+...+3/87.90)
A=2.(1/15-1/18+1/18-1/21/+...+1/87-1/90)
A=2.(1/15-1/90)
A=2.1/18
A=1/9
Bài 8:
a) Để A có giá trị nguyên thì \(n-5⋮n+1\)
\(\Leftrightarrow n+1-6⋮n+1\)
mà \(n+1⋮n+1\)
nên \(-6⋮n+1\)
\(\Leftrightarrow n+1\inƯ\left(-6\right)\)
\(\Leftrightarrow n+1\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)
hay \(n\in\left\{0;-2;1;-3;2;-4;5;-7\right\}\)
Vậy: \(n\in\left\{0;-2;1;-3;2;-4;5;-7\right\}\)
b) Để A có giá trị là phân số thì \(n-5⋮̸n+1\)
hay \(n\notin\left\{0;-2;1;-3;2;-4;5;-7\right\}\)
Bài 1:
1) \(\left(-7\right).21=\left(-147\right)\)
2) \(\dfrac{-7}{23}.\dfrac{11}{13}+\dfrac{-7}{23}.\dfrac{2}{13}-\dfrac{16}{23}\)
\(=\dfrac{-7}{23}.\left(\dfrac{11}{13}+\dfrac{2}{13}\right)-\dfrac{16}{23}\)
\(=\dfrac{-7}{23}.1-\dfrac{16}{23}\)
\(=\dfrac{-7}{23}-\dfrac{16}{23}\)
\(=\dfrac{-23}{23}=-1\)