\(S=\frac{1}{4}\times\left(\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+...+\frac{4}{41\times45}\right)\)

\(S=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)\)

\(S=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{45}\right)\)

\(S=\frac{1}{4}\times\frac{8}{45}\)

\(S=\frac{1\times2}{1\times45}\)

\(S=\frac{2}{45}\)

Vậy \(S=\frac{2}{45}\)

Tk nha bn !!

\(\frac{8}{135}\) nhé

mình nhầm , kết quả là \(\frac{2}{45}\)

\(S=\dfrac{1}{5\times9}+\dfrac{1}{9\times13}+...+\dfrac{1}{41\times45}\)

\(\Rightarrow4S=\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+...+\dfrac{4}{41\times45}\)

\(\Rightarrow4S=\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}\)

\(\Rightarrow4S=\dfrac{1}{5}-\dfrac{1}{45}\)

\(\Rightarrow4S=\dfrac{8}{45}\)

\(\Rightarrow S=\dfrac{2}{45}\)

\(=\dfrac{1}{4}\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{41\cdot45}\right)\)

\(=\dfrac{1}{4}\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{8}{45}=\dfrac{2}{45}\)

3/(1×5) + 3/(5×9) + 3/(9×13) + 3/(13×17) + 3/(17×21)

= 3/4 × (1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17 + 1/17 - 1/21)

= 3/4 × (1 - 1/21)

= 3/4 × 20/21

= 5/7

tới chỉ ghi đáp án thôi nhé

x=15

\(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+...+\dfrac{1}{45\times49}\)

\(=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{45\times49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{45}-\dfrac{1}{49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{49}\right)=\dfrac{1}{4}\times\dfrac{48}{49}=\dfrac{12}{49}\)

\(\Rightarrow\dfrac{7}{x}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{29}{45}\left(x\ne0\right)\\ \Rightarrow\dfrac{7}{x}+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{29}{45}\\ \Rightarrow\dfrac{7}{x}+\dfrac{8}{45}=\dfrac{29}{45}\\ \Rightarrow\dfrac{7}{x}=\dfrac{21}{45}\Rightarrow\dfrac{21}{3x}=\dfrac{21}{45}\Rightarrow3x=45\\ \Rightarrow x=15\)

Lời giải:

$12A=1.5.12+5.9.(13-1)+9.13(17-5)+13.17(21-9)+....+77.81(85-73)+81.85(89-77)$

$=60+(5.9.13+9.13.17+13.17.21+...+77.81.85+81.85.89)-(1.5.9+5.9.13+9.13.17+...+73.77.81+77.81.85)$

$=60+81.85.89 - 1.5.9=612780$

A = 1.5 + 5.9 + 9.13 + ... + 81.85

A = \(\dfrac{12}{12}\)(1.5 + 5.9 + 9.13 + 81.85)

A = \(\dfrac{1}{12}\).(1.5.12 + 5.9.12.+ 9.13.12 + ...+ 81.85.12]

A = \(\dfrac{1}{12}\).[1.5.(9 + 3) + 5.9.(13 - 1) + 9.13.(17 - 5) +...+ 81.85.(89 - 77)]

^{A = \(\dfrac{1}{12}\).[1.5.9 + 1.3.5 + 5.9.13 - 5.9.1 + 9.13.17 - 9.13.5 + ...+ 81.85.89 - 81.85.77]}

A = \(\dfrac{1}{12}\).[1.3.5 + 81.85.89]

A = \(\dfrac{1}{12}\).[15 + 612765]

A = \(\dfrac{1}{12}\).612780

A = 51065

Đặt \(A=\frac{7}{1\cdot5}+\frac{7}{5\cdot9}+\frac{7}{9\cdot13}+\frac{7}{13\cdot17}+\frac{7}{17\cdot21}\)

\(\frac{4}{7}A=\frac{4}{7}\left(\frac{7}{1\cdot5}+\frac{7}{5\cdot9}+\frac{7}{9\cdot13}+\frac{7}{13\cdot17}+\frac{7}{17\cdot21}\right)\)

\(\frac{4}{7}A=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)

\(\frac{4}{7}A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}\)

\(\frac{4}{7}A=1-\frac{1}{21}\)

\(\frac{4}{7}A=\frac{20}{21}\)

\(A=\frac{20}{21}:\frac{4}{7}=\frac{20}{21}\cdot\frac{7}{4}=\frac{5}{3}\)

Đặt biểu thức trên là A

\(\frac{4xA}{7}=\frac{4}{1x5}+\frac{4}{5x9}+\frac{4}{9x13}+\frac{4}{13x17}+\frac{4}{17x21}\)

\(\frac{4xA}{7}=\frac{5-1}{1x5}+\frac{9-5}{5x9}+\frac{13-9}{9x13}+\frac{17-13}{13x17}+\frac{21-17}{17x21}\)

\(\frac{4xA}{7}=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}\)

\(\frac{4xA}{7}=1-\frac{1}{21}=\frac{20}{21}\Rightarrow A=\frac{20}{21}.\frac{7}{4}=\frac{5}{3}\)