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

\(\dfrac{4\times x}{1\times5}\) + \(\dfrac{4\times x}{5\times9}\) + \(\dfrac{4\times x}{9\times13}\) + \(\dfrac{4\times x}{13\times17}\) = 16

\(x\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+\dfrac{4}{13\times17}\right)\) = 16

\(x\) \(\times\) (\(\dfrac{1}{1}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{13}\) + \(\dfrac{1}{13}\) - \(\dfrac{1}{17}\)) = 16

\(x\) \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{17}\)) = 16

\(x\) \(\times\) \(\dfrac{16}{17}\)  = 16

\(x\)            = 16 : \(\dfrac{16}{17}\)

\(x\)             = 17 

Đáp án + Giải thích các bước giải:

7/1×5+7/5×9+7/9×13+7/13×17+7/17×21

=7/4×(4/1×5+4/5×9+4/9×13+4/13×17+4/17×21)

=7/4×(1−1/5+1/5−1/9+1/9−1/13+1/13−1/17+1/17−1/21)

=7/4×(1+0+0+0+0−1/21)

=7/4×(1−1/21)

=7/4×2021

=5/3

nhớ tick nha

\(\dfrac{7}{1\times5}+\dfrac{7}{5\times9}+\dfrac{7}{9\times13}+\dfrac{7}{13\times17}\)\(+\) \(\dfrac{7}{17\times21}\)

= \(\dfrac{7}{4}\times\)( \(\dfrac{4}{1\times5}\)\(+\) \(\dfrac{4}{5\times9}\)\(+\) \(\dfrac{4}{9\times13}\)\(+\)\(\dfrac{4}{13\times17}\)\(+\)\(\dfrac{4}{17\times21}\))

= 7 \(\times\)(\(\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{17}-\dfrac{1}{21}\))

= 7\(\times\)(\(\dfrac{1}{1}-\dfrac{1}{21}\))

= \(\dfrac{7}{4}\)\(\times\) \(\dfrac{20}{21}\)

= \(\dfrac{5}{3}\)

5/3

7/1x5+7/5x9+7/9x13+7/13x17+7/17x21=75,5 120 1609

ஜ۩۞۩ஜ Ủng hộ tui nhaaaa ஜ۩۞۩ஜ 

 Ai đi qua xin để lại 1 k !!!!!!

tới chỉ ghi đáp án thôi nhé

x=15

4/5x9 + 4/9x13 + 4/13x17 + 4/ 17x21 + 4/ 21x25=27.911628241

Ta có:

\(\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+\frac{4}{17\times21}+\frac{4}{21\times25}\)

= \(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}+\frac{1}{21}-\frac{1}{25}\)

= \(\frac{1}{5}-\left(\frac{1}{9}+\frac{1}{9}\right)-\left(\frac{1}{13}-\frac{1}{13}\right)-\left(\frac{1}{17}-\frac{1}{17}\right)-\left(\frac{1}{21}-\frac{1}{21}\right)-\frac{1}{25}\)

= \(\frac{1}{5}-\frac{1}{25}\)

= \(\frac{5}{25}-\frac{1}{25}=\frac{4}{25}\)

#)Giải :

Đặt \(A=\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+\frac{1}{17.21}+\frac{4}{21.25}\)

\(A=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}+\frac{1}{21}-\frac{1}{25}\)

\(A=\frac{1}{5}-\frac{1}{25}\)

\(A=\frac{4}{25}\)

\(A=\frac{7}{1\cdot5}+\frac{7}{5\cdot9}+...+\frac{7}{17\cdot21}=\)

\(\frac{4}{7}A=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+...+\frac{4}{17\cdot21}=\)

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

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

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

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

\(A=\frac{20}{21}\times\frac{7}{4}=\frac{140}{84}=\frac{5}{3}\)

\(\frac{7}{1.5}+\frac{7}{5.9}+\frac{7}{9.13}+...+\frac{7}{17.21}\)

\(=\frac{7}{4}.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{17.21}\right)\)

\(=\frac{7}{4}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{17}-\frac{1}{21}\right)\)

\(=\frac{7}{4}.\left(1-\frac{1}{21}\right)\)

\(=\frac{7}{4}.\frac{20}{21}=\frac{5}{3}\)

 1/5 + 1/45 + 1/117 + 1/221 + 1/357+ .... + 1/159197

Đặt A=1/5 + 1/45 + 1/117 + 1/221 + 1/357+ .... + 1/159197

      A= 1/1x5 + 1/5x9 + 1/9x13 + 1/13x17 + .... + 1/397x401

   Ax4=4/1x5 + 4/5x9 + 4/9x13 + 4/13x17 + .... + 4/397x401

   Ax4=(1-1/5) + (1/5-1/9) + (1/9-1/13)+….+(1/397-1/401)

   Ax4=1-1/401

       A=100/401

Mà 1/4=100/400>100/401=A nên A<1/4.