\(A=\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{21.23}\)
A=\(\frac{1}{3}\left(1-\frac{1}{3}+\frac{1}{3}-.......-\frac{1}{23}\right)\)=\(\frac{1}{3}.\frac{22}{23}=\frac{22}{69}\)
hok t
tl lại
\(A=\frac{1}{1.3}+....\frac{1}{21.23}\)
\(A=\frac{1}{2}\left(1-\frac{1}{3}+.....+\frac{1}{21}-\frac{1}{23}\right)\)
\(A=\frac{1}{2}.\frac{22}{23}=\frac{11}{23}\)
k t nha
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{483}\)
\(=\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{21\times23}\)
\(=\frac{1}{2}\times[2\times\left(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{21\times23}\right)]\)
\(=\frac{1}{2}\times\left(\frac{2}{1\times3}\times\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{21\times23}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{21}-\frac{1}{23}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{23}\right)\)
\(=\frac{1}{2}\times\frac{22}{23}\)
\(=\frac{11}{23}\)
Nhớ h cho mk nha
