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28 tháng 7 2017

đáp số cuối cùng là 0 vì 1-1/4 = 0/4 = 0 x cho những số nào khác cũng bằng 0 thôi

28 tháng 7 2017

\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{10000}\right)\)

\(=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{999}{10000}\)

\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times...\times\frac{99\times101}{100\times100}\)

\(=\frac{1}{2}\times\frac{101}{100}\)

\(=\frac{101}{200}\)

\(\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right).....\left(1-\dfrac{1}{10000}\right)\)

\(=\dfrac{2^2-1}{2^2}\cdot\dfrac{3^2-1}{3^2}\cdot\dfrac{4^2-1}{4^2}\cdot\cdot\cdot\dfrac{100^2-1}{100^2}\)

\(=\dfrac{1.3.2.4.3.5.....99.101}{2.2.3.3.4.4....100.100}\)

\(=\dfrac{\left(1.2.3...99\right)}{2.3.4....100}\cdot\dfrac{3.4.5...101}{2.3.4....100}=\dfrac{1}{100}\cdot\dfrac{101}{2}=\dfrac{101}{200}\)

Ta có: \(\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\cdot...\cdot\left(1-\dfrac{1}{10000}\right)\)

\(=\dfrac{-3}{4}\cdot\dfrac{-8}{9}\cdot\dfrac{-15}{16}\cdot...\cdot\dfrac{-9999}{10000}\)

\(=-\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{9999}{10000}\)

\(=\dfrac{-3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot1111\cdot9}{2^2\cdot3^2\cdot4^2\cdot...\cdot100^2}\)

\(=\dfrac{101}{200}\)

`(1-1/4) \times (1-1/9) \times (1-1/16) \times ... \times (1-1/10000)`

`= 3/4 \times 8/9 \times 15/16 \times ... \times 9999/10000`

`= (3 \times 8 \times 15 \times ... \times 9999)/(4 \times 9 \times 16 \times ... \times 10000)`

`=`\(\dfrac{\left(1\times3\right)\times\left(2\times4\right)\times\left(3\times5\right)\times...\times\left(99\times101\right)}{\left(2\times2\right)\times\left(3\times3\right)\times\left(4\times4\right)\times...\times\left(100\times100\right)}\)

`=` \(\dfrac{\left(1\times2\times3\times...\times99\right)\times\left(3\times4\times5\times...\times101\right)}{\left(2\times3\times4\times...\times100\right)\times\left(2\times3\times4\times...\times100\right)}\)

`=` \(\dfrac{1\times101}{2\times100}\)

`= 101/200.`

(1-1/4) x ( 1-1/9) x ( 1- 1/16) x....x (1 - 1/10000)

= 3/4 x 8/9 x 15/16 x ... x 9999/10000

= (1x3/2x2) x ( 2x4/3x3 ) x ( 3 x 5 / 4x4 ) x ... x ( 99 x 101 / 100x 100 )

\(\dfrac{\left(1.2.3...99\right).\left(3.4.5.101\right)}{\left(2.3.4...100\right).\left(2.3.4...100\right)}\)

= 1 x 101 / 100 x 2

= 101/200

6 tháng 8 2015

A = ( 1 - 1/4 ) x ( 1 - 1/9 ) x .... x ( 1 - 1/10000 )

 

24 tháng 2 2017

13/25

12 tháng 4 2017

0,52 ban a

\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)

\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)

\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)

\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)