Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Nhưng bn ơiX là x^2 hay tách biệt nếu tách biệt thì là 9/49 còn nếu là x^2 thì là 3/7 nhé
\(=\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)xX=\frac{9}{7} \)\(=\left(\frac{1}{3}-\frac{1}{21}\right)xX=\frac{9}{7}\)\(=\frac{2}{7}xX=\frac{9}{7}\)
\(X=\frac{9}{7}:\frac{2}{7}\)
\(X=\frac{9}{2}\)
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\)\(...+\frac{2}{8.9}+\frac{2}{9.10}\)
Đặt \(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(B=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}+\frac{2}{9.10}\)
Ta có:
\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(A=\frac{1}{3}-\frac{1}{15}\)
\(A=\frac{4}{15}\)
\(B=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}+\frac{2}{9.10}\)
\(B=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(B=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(B=2\left(1-\frac{1}{10}\right)\)
\(B=2.\frac{9}{10}\)
\(B=\frac{9}{5}\)
\(\Rightarrow A+B=\frac{4}{15}+\frac{9}{5}\)
\(=\frac{31}{15}\)
Vậy biểu thức trên có giá trị là \(\frac{31}{15}\)
=2/5-2/7+ 2/7-2/9+2/9-2/11+2/11-2/13+2/13-2/15
=2/5-(2/7-2/7)-(2/9-2/9)-(2/11-2/11)-(2/13-2/13)-2/15
=2/5-0-0-0-0-2/15
=2/5-2/15
4/15
\(B=\frac{4}{1\times3}+\frac{4}{3\times5}+...+\frac{4}{9\times11}+\frac{4}{11\times13}\)
\(=2\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{9\times11}+\frac{2}{11\times13}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=2\times\left(1-\frac{1}{13}\right)\)
\(=2\times\frac{12}{13}\)
\(=\frac{24}{13}\)
B = \(\frac{4}{1.3}+\frac{4}{3.5}+...+\frac{4}{11.13}\)
\(=4\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{11.13}\right)\)
\(=4.\frac{1}{4}.\left(\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{11}-\frac{2}{13}\right)\)
\(=2-\frac{2}{13}=\frac{24}{13}\)
A = \(\dfrac{4}{1\times3}\) - \(\dfrac{8}{3\times5}\) + \(\dfrac{12}{5\times7}\) - \(\dfrac{16}{7\times9}\) + \(\dfrac{20}{9\times11}\) - \(\dfrac{24}{11\times13}\)
A = ( \(\dfrac{1}{1}+\dfrac{1}{3}\)) - ( \(\dfrac{1}{3}\) + \(\dfrac{1}{5}\)) + (\(\dfrac{1}{5}\)+ \(\dfrac{1}{7}\)) - ( \(\dfrac{1}{7}\) + \(\dfrac{1}{9}\)) +( \(\dfrac{1}{9}\)+ \(\dfrac{1}{11}\)) - (\(\dfrac{1}{11}\)+\(\dfrac{1}{13}\))
A = \(\dfrac{1}{1}+\dfrac{1}{3}\) - \(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{7}\) - \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{11}\) - \(\dfrac{1}{13}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{13}\)
A = \(\dfrac{12}{13}\)
=2/11+2/13-2/13+2/15-2/15+...-2/97+2/98
=2/11+(2/13-2/13+2/15-2/15+...-2/97+2/99)
=2/11+2/99
=20/99
\(\frac{2}{11}\times13+\frac{2}{13}\times15+\frac{2}{15}\times17+........+\frac{2}{97}\times99\)
\(A\times2=\frac{2}{11\times13}+\frac{2}{13\times15}+\frac{2}{15\times17}+........+\frac{2}{97\times99}\)
\(A\times2=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+........+\frac{1}{97}-\frac{1}{99}\)
\(A=\frac{1}{11}-\frac{1}{99}\)
\(A=\frac{8}{99}\)
mik ko bt là có đúng hay ko nhưng đúng thì các bạn cho 1 t i c k nha
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
Ta có:
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+....+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\frac{10}{231}-x+\frac{221}{231}=\frac{4}{3}\)
\(\frac{10}{231}-x=\frac{4}{3}-\frac{221}{231}=\frac{29}{77}\)
\(x=\frac{10}{231}-\frac{29}{77}\)
\(x=-\frac{1}{3}\)
2/(7 × 9) + 2/(9 × 11) + 2/(11 × 13) + ... + 2/(97 × 99)
= 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + ... + 1/97 - 1/99
= 1/7 - 1/99
= 92/693
\(\dfrac{4}{9\cdot11}+\dfrac{4}{11\cdot13}+...+\dfrac{4}{97\cdot99}\)
\(=2\left(\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}+...+\dfrac{2}{97\cdot99}\right)\)
\(=2\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{10}{99}=\dfrac{20}{99}\)