( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16 ) x ( 1 - 1/25 ) x ( 1 - 1/36 )
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)
\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)
\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)
\(=\)\(\text{}\text{}\text{}\text{}\text{}\text{}\frac{\text{}\text{}\text{}\text{}\text{}\text{}3\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times7}{4\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times8\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times6}\)
\(=\)\(\frac{7\text{}\text{}\text{}\times4}{8\times6}\)
\(=\)\(\frac{7\times4}{4\times2\times6}\)
\(=\)\(\frac{7}{2\times6}\)
\(=\)\(\frac{7}{12}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(K=\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)
\(K=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x\frac{35}{36}\)
tự rút gọn
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}=\frac{3.8.15.24.35}{4.9.16.25.36}=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}\)
\(=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{2.2}=\frac{7}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đề bài bạn viết khó hiểu quá. Bạn nên viết lại rõ ràng, mạch lạc, có ngắt nghỉ và xuống dòng hợp lý.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)=\frac{8}{5}\)
\(A\times\frac{3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times\frac{4\times6}{5\times5}=\frac{8}{5}\)
\(A\times\frac{3\times2\times4\times3\times5\times4\times6}{2\times2\times3\times3\times4\times4\times5\times5}=\frac{8}{5}\)
\(A\times\frac{6}{2\times5}=\frac{8}{5}\)
\(A\times\frac{3}{5}=\frac{8}{5}\)
\(A=\frac{8}{5}:\frac{3}{5}\)
\(A=\frac{8}{3}\)
ta có:
A = 8/5 : [(1 - 1/4) x ... x (1 - 1/5)]
= 8/5 : [3/4 x 8/9 x 15/16 x 24/25]
= 8/5 : 3/5
= 8/5 x 5/3
= 8/3
... là như đề bài nha!
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