Bài 1 :

\(A=\dfrac{n+1}{n+2}\) có giá trị nguyên âm, dương khi

\(n+1⋮n+2\)

\(\Rightarrow n+1-\left(n+2\right)⋮n+2\)

\(\Rightarrow n+1-n-2⋮n+2\)

\(\Rightarrow-1⋮n+2\)

\(\Rightarrow n+2\in\left\{-1;1\right\}\)

\(\Rightarrow n\in\left\{-3;-1\right\}\left(n\in Z\right)\)

Bài 2 :

\(1+\left(-\dfrac{1}{60}\right)+\dfrac{19}{120}< \dfrac{x}{36}+\left(-\dfrac{1}{60}\right)< \dfrac{58}{90}+\dfrac{59}{72}+\left(-\dfrac{1}{60}\right)\)

\(\Rightarrow1+\dfrac{19}{120}< \dfrac{x}{36}< \dfrac{58}{90}+\dfrac{59}{72}\)

\(\Rightarrow\dfrac{139}{120}< \dfrac{x}{36}< \dfrac{232}{360}+\dfrac{295}{360}\)

\(\Rightarrow\dfrac{417}{360}< \dfrac{10x}{360}< \dfrac{527}{360}\)

\(\Rightarrow417< 10x< 527\)

\(\Rightarrow10x\in\left\{420;430;440;450;460;470;480;490;500;510;520\right\}\)

\(\Rightarrow x\in\left\{42;43;44;45;46;47;48;49;50;51;52\right\}\)

Ta có:

1+2+3-4-5-6+7+8+9-..........+55+56+57-58-59-60

=(1+2+3-4-5-6)+(7+8+9-10-11-12)..........+(55+56+57-58-59-60)

=  -3+ (-3)+...+(-3)

---12 số------------

=(-3).12

=-36

Ta có

Do đó, hai đại lượng x và y không tỉ lệ thuận với nhau.

\(3A=\frac{3}{2.3}+\frac{3}{6.3}+\frac{1}{12.3}+\frac{3}{20.3}+\frac{3}{30.3}+\frac{3}{42.3}\)

\(3A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(3A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}\)

\(3A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)

\(3A=1-\frac{1}{7}=\frac{6}{7}\Rightarrow A=\frac{2}{7}\)