Ta có:

\(P=\frac{2-n}{n-1}=\frac{-n+2}{n-1}=\frac{-\left(n-1\right)+1}{n-1}=-1+\frac{1}{n-1}.\)

Để P là số nguyên thì \(n-1\inƯ\left(1\right)=\left\{1,-1\right\}\)

n - 1 = 1 => n = 2

n - 1 = -1 => n = 0

Vậy \(n\in\left\{2;0\right\}\)Thì P là số nguyên

Trả lời

\(\frac{31}{17}+\left(\frac{-5}{13}\right)+\left(\frac{-8}{13}\right)-\frac{4}{17}\)

\(=\left(\frac{31}{17}-\frac{4}{17}\right)+\left[\left(\frac{-5}{13}\right)+\left(\frac{-8}{13}\right)\right]\)

\(=\frac{27}{17}+\left(\frac{-13}{13}\right)\)

\(=\frac{27}{17}+\left(-1\right)\)

\(=\frac{10}{17}\)

\(\frac{31}{17}+\frac{-5}{13}+\frac{-8}{13}-\frac{4}{17}\)

\(=\left(\frac{31}{17}-\frac{4}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)\)

\(=\frac{27}{13}+\frac{-13}{13}\)

\(=\frac{27}{13}+\left(-1\right)\)

\(=\frac{10}{17}\)

tại sao 9,75 giờ = 9 giờ 45 phút

Trả lời

Ta có:

\(C=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{9999}{10000}\)

\(\Rightarrow C=\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{9}\right)+\left(1-\frac{1}{16}\right)+...+\left(1-\frac{1}{10000}\right)\)

\(\Rightarrow C=\left(1+1+1+...+1\right)-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{10000}\right)\)(99 chữ số 1)

\(\Rightarrow C=99-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{10000}\right)\)

Ta lại có:

\(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{10000}=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)

Đặt D\(=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)

\(\Rightarrow D< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(\Rightarrow D< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow D< 1-\frac{1}{100}\)

\(\Rightarrow D< \frac{99}{100}< 1\)

\(\Rightarrow C>99-1\)

\(\Rightarrow C>98\)

Vậy C>98 (đpcm)

Su. Tu lam gi an  co

sư tử làm gì ăn cỏ 

x/1.4+x/4.7+x/7.10+x/10.13+x/13.16=5/2

=>x/3(1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)=5/2

=>x/3.(1/4-1/16)=5/2

=>x/3.3/16=5/2

=>x/3=5/2:3/16

=>x/3=40/3

=>x=40

Vậy x=40

\(a,\frac{7}{12}\cdot\frac{6}{11}+\frac{7}{12}\cdot\frac{5}{11}+2\frac{7}{12}\)

\(=\frac{7}{12}\cdot\left(\frac{6}{11}+\frac{5}{11}\right)+2\frac{7}{12}\)

\(=\frac{7}{12}+\frac{31}{12}\)

\(=\frac{38}{12}=\frac{19}{6}\)

\(b,\frac{-5}{9}\cdot\frac{-6}{13}+\frac{5}{-9}\cdot\frac{-5}{13}-\frac{5}{9}\)

\(=\frac{-5}{9}\cdot\frac{-6}{13}+\frac{-5}{9}\cdot\frac{-5}{13}+\frac{-5}{9}\cdot1\)

\(=\frac{-5}{9}\cdot\left(\frac{-6}{13}+\frac{-5}{13}+1\right)\)

\(=\frac{-5}{9}\cdot\left(\frac{-11}{13}+1\right)\)

\(=\frac{-5}{9}\cdot\frac{2}{13}\)

\(=\frac{-10}{117}\)

\(c,\)\(0,8\cdot\frac{-15}{14}-\frac{4}{5}\cdot\frac{13}{14}-1\frac{2}{5}\)

\(=\frac{4}{5}\cdot\frac{-15}{14}-\frac{4}{5}\cdot\frac{13}{14}-\frac{7}{5}\)

\(=\frac{4}{5}\cdot\left(\frac{-15}{14}-\frac{13}{14}\right)-\frac{7}{5}\)

\(=\frac{4}{5}\cdot\left(-2\right)-\frac{7}{5}\)

\(=\frac{-8}{5}-\frac{7}{5}\)

\(=-3\)

\(d,\)\(75\%\cdot\frac{6}{7}+5\%\cdot\frac{6}{7}+\frac{7}{10}\cdot1\frac{1}{7}\)

\(=\frac{3}{4}\cdot\frac{6}{7}+\frac{1}{20}\cdot\frac{6}{7}+\frac{7}{10}\cdot\frac{8}{7}\)

\(=\left(\frac{3}{4}+\frac{1}{20}\right)\cdot\frac{6}{7}+\frac{7}{10}\cdot\frac{8}{7}\)

\(=\frac{4}{5}\cdot\frac{6}{7}+\frac{4}{5}\cdot1\)

\(=\frac{4}{5}\cdot\left(\frac{6}{7}+1\right)\)

\(=\frac{4}{5}\cdot\frac{13}{7}\)

\(=\frac{52}{35}\)