\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{575}\)

\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{23.25}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{23}-\frac{1}{25}\)

\(=\frac{1}{3}-\frac{1}{25}=\frac{22}{75}\)

Bài làm:

c) \(\left(x-2\right)\left(x+3\right)>0\)

Ta xét 2 trường hợp sau:

+ Nếu \(\hept{\begin{cases}x-2>0\\x+3>0\end{cases}\Rightarrow}\hept{\begin{cases}x>2\\x>-3\end{cases}\Rightarrow}x>2\)

+ Nếu \(\hept{\begin{cases}x-2< 0\\x+3< 0\end{cases}}\Rightarrow\hept{\begin{cases}x< 2\\x< -3\end{cases}}\Rightarrow x< -3\)

Vậy \(\orbr{\begin{cases}x>2\\x< -3\end{cases}}\)

d) \(-1\frac{5}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\)

\(\Leftrightarrow-\frac{32}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\)

\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=-\frac{8}{27}\)

\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=\left(-\frac{2}{3}\right)^3\)

\(\Rightarrow3x-\frac{7}{9}=-\frac{2}{3}\)

\(\Leftrightarrow3x=\frac{1}{9}\)

\(\Leftrightarrow x=\frac{1}{27}\)

Vậy \(x=\frac{1}{27}\)

Học tốt!!!!

a) nhầm cái (1/2020-1) thành (1/2017-1) rồi nha

(1/2-1)*(1/3-1)*...*(1/2019-1)*(1/2020-1)

= (-1/2)*(-2/3)*...*(-2018/2019)*(-2019/2020)

= (-1)*(-2)*...*(-2019)/2*3*...*2019*2020

=(-1)*(-1)*...*(-1)/2020

=-1/2020 (vì từ 1-> 2019 có 2019 số hạng)

b) 1/6+1/12+1/20+1/30+1/42+1/56

=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

=1-1/8=7/8