\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{399}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\)
\(=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=\frac{1}{2}.\left(\frac{7}{21}-\frac{1}{21}\right)\)
\(=\frac{1}{2}.\frac{6}{21}\)
\(=\frac{1}{7}\)
Chúc bạn học tốt !!!
\(A=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{399}\)
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)
\(2A=\frac{1}{3}-\frac{1}{21}=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}=\frac{2}{7}\)
\(A=\frac{2}{7}:2=\frac{2}{7}.\frac{1}{2}=\frac{2}{14}=\frac{1}{7}\)
Trả lời
Đặt A=\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{399}\)
\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{19\cdot21}\)
\(2A=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{19\cdot21}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)
\(2A=\frac{1}{3}-\frac{1}{21}\)
\(2A=\frac{6}{21}\Rightarrow A=\frac{6}{21}:2\Rightarrow A=\frac{1}{7}\)
\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{399}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}=\frac{6}{21}=\frac{2}{7}\)
\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{399}\)
\(=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{19\times21}\)
\(=\frac{1}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{19\times21}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=\frac{1}{2}\times\frac{6}{21}\)
\(=\frac{1}{7}\)
\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{399}\)
Đặt biểu thức trên là A.
A= \(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{19x21}\)
Ax2= \(\left(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{19x21}\right)x2\)
Ax2= \(\frac{2}{2x5}+\frac{2}{5x7}+\frac{2}{7x9}+...+\frac{2}{19x21}\)
Ax2= \(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
Ax2= \(\frac{1}{2}-\frac{1}{21}\)
Ax2= \(\frac{19}{42}\)
A=
\(\frac{19}{42}:2=\frac{19}{84}\)
1/15+1/35+1/63+...+1/399
= 1/3x5+1/5x7+1/7x9+...+1/19x21
= 2(1/3-1/5+1/5-1/7+1/7-1/9+...+1/19-1/21)
= 2 x 1/3 + 1/21
= 2 x 7/21 + 1/21
= 2 x 8/21
=16/21
chúc bạn học tốt nhớ k mk nha mk cần lên điểm hỏi đáp
Hãy chứng minh
1/2²+1/3²+1/4²+1/100²<3/4
