Tacó cho công thức tổng quát: A² - B² = (A+B).(A-B) 
A = (1-1/4)x(1-1/9)x(1-1/16)x(1-1/25)x(1-1/3... 
= (1+1/2) x (1-1/2) x (1+1/3) x (1-1/3) x...x (1+1/n) x (1-1/n) 
= (1+1/2) x (1+1/3) x (1+1/4) x ... x [1 + 1/(n-1) ] x (1 + 1/n) 
x (1-1/2) x (1-1/3) x (1-1/4) x ... x [1 - 1/(n-1) ] x (1 - 1/n) 
= 3/2 x 4/3 x 5/4 x ... x [ n/(n-1) ] x [ (n+1)/n ] 
x 1/2 x 2/3 x 3/4 x ... x [ (n-2)/(n-1) ] x [ (n-1)/n] 
               Vậy dãy A là:
A = 1/2 x 2/3 x 3/2 x 3/4 x 4/3 x 4/5 x 5/4 x .... x [ (n-2)x(n-1) ] x [ (n-1)/n] x [ n/(n-1)] x [ (n+1)/n] 
= 1/2 x 1 x 1 x 1 x ... x 1 x [(n+1)/n] 

giai bang cach lop 5

lời giải luôn nhé

\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)

\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)

\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)

\(=\)\(\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\frac{\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times2\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times7}{4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times8\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times2\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6}\)

\(=\)\(\frac{7\text{​​}\text{​​}\text{​​}\times4}{8\times6}\)

\(=\)\(\frac{7\times4}{4\times2\times6}\)

\(=\)\(\frac{7}{2\times6}\)

\(=\)\(\frac{7}{12}\)

\(K=\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)

\(K=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x\frac{35}{36}\)

tự rút gọn

thôi tui làm nốt cho

...

\(K=\frac{1x3}{2x2}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x\frac{4x6}{5x5}x\frac{5x7}{6x6}\)

\(K=\frac{7}{2}\)

K=3/4 x 8/9 x 15/16 x24/25x 35/36

k=7/12

giải giúp mk vs

\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)

\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}=\frac{3.8.15.24.35}{4.9.16.25.36}=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}\)

\(=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{2.2}=\frac{7}{4}\)

\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)

\(=\)\(\frac{3}{4}\) x      \(\frac{8}{9}\)    x        \(\frac{15}{16}\)   x      \(\frac{24}{25}\)    x      \(\frac{35}{36}\)

\(=\frac{7}{12}\)

P/S : Bài này mình vừa mới là cho Bạn Nguyễn Thu Trang 

dat off roi

3/4x8/9x15/16x24/25x35/36=7/12

on lai roi

có 2014 là số chẵn => 2014^x là số chẵn

có 4 là số chẵn => 4y là số chẵn

=> 2014^x+4y là số chẵn mà 2013 là số lẻ

=> không có giá trị của x,y dể 2014^y+4y=2013

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