\(\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{99.101}\)

\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{101}\right)\)

\(=2.\frac{96}{505}\)

\(=\frac{192}{505}\)

cho tao chết đi nhá

Đặt \(A=\frac{4}{3\times5}+\frac{4}{5\times7}+\frac{4}{7\times9}+...+\frac{4}{99\times101}\)

\(\Leftrightarrow\frac{1}{2}A=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{99\times101}\)

\(\Leftrightarrow\frac{A}{2}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)

\(\Leftrightarrow\frac{A}{2}=\frac{1}{3}-\frac{1}{101}\)

\(\Leftrightarrow\frac{A}{2}=\frac{98}{303}\)

\(\Leftrightarrow A=\frac{98}{303}\times2\)

\(\Leftrightarrow A=\frac{196}{303}\)

được lắm thằng cu ! tốt cho mày đúng rồi

\(A=\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{59.61}\)

\(A=2\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{59.61}\right)\)

\(A=2\left(\frac{7-5}{5.7}+\frac{9-7}{7.9}+\frac{11-9}{9.11}+...+\frac{61-59}{59.61}\right)\)

\(A=2\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{59}-\frac{1}{61}\right)\)

\(A=2\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{112}{305}\).

4/5x7 + 4/7x9 + 4/9x11 + ... + 4/50x61

= 2x(2/5x7 + 2/7x9 + 2/9x11 + ... + 2/59x61)

= 2x [(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+...+(1/59-1/61)]

= 2x(1/5-1/61)

= 2x 56/305

= 112/305

Gọi biểu thức đó là S nha.

S= 336/505

336/505

B=2/3x5 + 2/5x7 + 2/7x9 + ...+2/99x101

B= 1/3 - 1/5 + 1/5 - 1/7 + 1/7 -1/9 + ... + 1/99 - 1/101

B= 1/3 - 1/101

B=98/303

( k mk nhé ! Cách làm câu a và b của mk đều đúng 100% đấy ! Dạng này mk học từ lâu rồi ! )

a, A = 1/2x3+ 1/ 3x4 + 1/4x5 + 1/5x6 + ... + 1/99x100

    A= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 -1/5 + 1/5 - 1/6 + ... + 1/99 -1/100

    A= 1/2 -1/100

    A= 49 / 100

nhờ bạn giải dùm mình câu c,d

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 = \(\dfrac{12}{13}\)