\(S=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{78.79.80}\)

\(\Rightarrow S=\dfrac{79\left(79+3\right)}{4\left(79+1\right)\left(79+2\right)}\)

\(S=\dfrac{79.82}{4.80.81}=\dfrac{79.41}{160.81}=\dfrac{3239}{12960}\)

\(\text{2.24.25+3.31.16+6.2.8.17}\)

\(=\text{2.6.4.25+3.31.16+6.16.17}\)

\(=\text{12.100+16.3(31+2.17)}\)

\(=\text{1200+48(31+34)}=1200+48.65=1200+3120=4320\)

\(A=\dfrac{1}{3}-\left[\left(-\dfrac{5}{4}\right)-\left(\dfrac{1}{4}+\dfrac{3}{8}\right)\right]\)

\(A=\dfrac{1}{3}-\left[\dfrac{-5}{4}-\dfrac{5}{8}\right]=\dfrac{1}{3}-\left(\dfrac{-15}{8}\right)\)

\(A=\dfrac{53}{24}\)

=> A > 2

=> C là đáp án đúng

A

\(a^2=3b^2\)

Vì \(a^2;b^2\) là số chính phương

\(\Rightarrow a^2⋮̸3b^2\)

Nên không tồn tại a;b nguyên dương thỏa đẳng thức \(a^2=3b^2\)

Phần lỗi màu đỏ là a² không thể chia cho 3 có thương là b² là số chính phương

Bài này anh làm rồi ra 2/5 rồi đó em

Coi tổng kế hoạch tháng là 1

Để hoàn thành kế hoạch của tháng, trong tuần cuối nhà máy phải thực hiện: 1 -3/15 - 6/30 - 2/10=2/5 ( công việc)

Có ai không giúp mình với

\(B=\dfrac{5}{3.7}+\dfrac{5}{7.11}+\dfrac{5}{11.15}+...+\dfrac{5}{\left(4n-1\right)\left(4n+3\right)}\)

\(\Rightarrow B=5\left[\dfrac{1}{3.7}+\dfrac{1}{7.11}+\dfrac{1}{11.15}+...+\dfrac{1}{\left(4n-1\right)\left(4n+3\right)}\right]\)

\(\Rightarrow B=5.\dfrac{1}{4}\left[\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{4n-1}-\dfrac{1}{4n+3}\right]\)

\(\Rightarrow B=\dfrac{5}{4}\left(\dfrac{1}{3}-\dfrac{1}{4n+3}\right)\)

\(\Rightarrow B=\dfrac{5}{4}\left(\dfrac{4n+3-3}{3\left(4n+3\right)}\right)\)

\(\Rightarrow B=\dfrac{5}{4}\left(\dfrac{4n}{3\left(4n+3\right)}\right)\)

\(\Rightarrow B=\dfrac{5n}{12n+9}\Rightarrow dpcm\)

\(M=1+3^2+3^4+3^6+...+3^{112}\)

\(\Rightarrow3M=3+3^3+3^5+3^7+...+3^{113}\)

\(\Rightarrow3M+M=1+3^2+3^4+3^5+...+3^{113}\)

\(\Rightarrow4M=\dfrac{3^{113+1}-1}{3-1}\)

\(\Rightarrow M=\dfrac{3^{114}-1}{2.4}=\dfrac{3^{114}-1}{8}\)

`@` `\text {Ans}`

`\downarrow`

`4,`

`a)`

\(\dfrac{-1}{24}-\left[\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{8}\right)\right]\)

`=`\(\dfrac{-1}{24}-\left[\dfrac{1}{4}-\left(-\dfrac{3}{8}\right)\right]\)

`=`\(\dfrac{-1}{24}-\left(\dfrac{1}{4}+\dfrac{3}{8}\right)\)

`=`\(\dfrac{-1}{24}-\dfrac{5}{8}=-\dfrac{2}{3}\)

`b)`

\(\left(\dfrac{5}{7}-\dfrac{7}{5}\right)-\left[\dfrac{1}{2}-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)

`=`\(\dfrac{-24}{35}-\left[\dfrac{1}{2}-\left(-\dfrac{27}{70}\right)\right]\)

`=`\(\dfrac{-24}{35}-\left(\dfrac{1}{2}+\dfrac{27}{70}\right)\)

`=`\(\dfrac{-24}{35}-\dfrac{31}{35}=-\dfrac{55}{35}=-\dfrac{11}{7}\)

`c)`

\(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{71}-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)

`=`\(-\dfrac{1}{2}+\dfrac{3}{5}-\dfrac{1}{9}+\dfrac{1}{71}+\dfrac{2}{7}+\dfrac{4}{35}-\dfrac{7}{18}\)

`=`\(\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{71}\)

`=`\(\left(-\dfrac{9}{18}-\dfrac{2}{18}-\dfrac{7}{18}\right)+\left(\dfrac{21}{35}+\dfrac{10}{35}+\dfrac{4}{35}\right)+\dfrac{1}{71}\)

`=`\(-\dfrac{18}{18}+\dfrac{35}{35}+\dfrac{1}{71}=-1+1+\dfrac{1}{71}=\dfrac{1}{71}\)

`d)`

\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)

`=`\(3-\dfrac{1}{4}+\dfrac{2}{3}-5+\dfrac{1}{3}+\dfrac{6}{5}-6+\dfrac{7}{4}-\dfrac{3}{2}\)

`=`\(\left(3-5-6\right)+\left(-\dfrac{1}{4}+\dfrac{7}{4}-\dfrac{3}{2}\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\dfrac{6}{5}\)

`=`\(-8+0+\dfrac{3}{3}+\dfrac{6}{5}\)

`=`\(-8+1+\dfrac{6}{5}\)

`=`\(-7+\dfrac{6}{5}=-\dfrac{29}{5}\)

giúp mik lm câu 4 vs ạ