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

\(G=2^{2x+1}+4^{x+3}=264\\\Leftrightarrow 2^{2x+1}+\left(2^2\right)^{x+3}=264\\ \Leftrightarrow2^{2x+1}+2^{2x+6}=264\\ \Leftrightarrow2^{2x+1}\left(1+2^5\right)=264\\ \Leftrightarrow2^{2x+1}.33=264\\ \Leftrightarrow2^{2x+1}=\dfrac{264}{33}=8=2^3\\ Vậy:2x+1=3\\ \Rightarrow2x=3-1=2\\ x=\dfrac{2}{2}=1\\ Vậy:x=1\)

___

\(h,\dfrac{x-1}{x+2}=\dfrac{4}{5}\left(ĐK:x\ne2\right)\\ \Rightarrow5\left(x-1\right)=4\left(x+2\right)\\ \Leftrightarrow5x-4x=8+5\\ \Leftrightarrow x=13\\ Vậy:x=13\)

\(45p=\dfrac{3}{4}\left(giờ\right)\)

Khoảng cách từ Hải Phòng ra Cát Bà là :

\(1,852.30.\dfrac{3}{4}=41,67\left(km\right)\)

Độ chính xác 0,5 nên \(41,67km\rightarrow42km\)

Đáp số 42 km

             Đổi 45 phút = \(\dfrac{3}{4}\)giờ

Khoảng cách từ Hải Phòng đến đảo Cát Bà là: 

         1,852.30.\(\dfrac{3}{4}\)=41,67 (km)

                   Đ/S:...

Bạn xem lại đề

Xét tam giác ABC, có:ˆA1+ˆB+ˆC1=1800 (Tổng các góc của tam giác)Xét tam giác ADC, có:ˆA2+ˆD+ˆC2=1800 (Tổng các góc của tam giác)Xét tứ giác ABCD, có:ˆA+ˆB+ˆD+ˆC=ˆA1+ˆA2+ˆB+ˆD+ˆC1+ˆC2=(ˆA1+ˆB+ˆC1)+(ˆA2+ˆD+ˆC2)=1800+1800=3600⇒đpcm

\(3^8.9^2=3^8.\left(3^2\right)^2=3^8.3^4=3^{8+4}=3^{12}\)

Lần sau nên chọn đúng môn.