(1/4 - 1)*(1/9 - 1)*(1/16 - 1).....(1/10000 - 1)
tính dùm cái
tính : A= (1-1/4) . (1-1/9) . (1-1/16) ...(1-1/10000)
tính A = (1-1/4)*(1-1/9)*(1-1/16)*(1-1/16)*...(1-1/10000)
Ta có: \(1-\frac{1}{4}=\frac{3}{4}=\frac{1}{2}.\frac{3}{2}\); \(1-\frac{1}{9}=\frac{8}{9}=\frac{2}{3}.\frac{4}{3}\); \(1-\frac{1}{16}=\frac{15}{16}=\frac{3}{4}.\frac{5}{4}\);
...; \(1-\frac{1}{10000}=\frac{9999}{10000}=\frac{99}{100}.\frac{101}{100}\)
=> \(A=\frac{1}{2}.\frac{3}{2}.\frac{2}{3}.\frac{4}{3}.\frac{3}{4}.\frac{5}{4}....\frac{99}{100}.\frac{101}{100}\). Nhận thấy; Tích của 2 số liền kề thì bằng 1
=> \(A=\frac{1}{2}.\frac{101}{100}=\frac{101}{200}\)
Đáp số: \(A=\frac{101}{200}\)
Tính các tích sau:
A=3/4 . 8/9 .15/16 . ..... . 9999/10000
B=(1 - 1/4)(1 - 1/9). ..... . (1 - 1/10000)
C=(1 + 1/1.3)(1 + 1/2.4)(1 + 1/3.15). ..... .(1 + 1/99.100)
A=\(\dfrac{3}{4}.\dfrac{8}{9}.....\dfrac{9999}{10000}\)
A=\(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.....\dfrac{99.101}{100.100}\)
A=\(\dfrac{1.2.3.....99}{2.3.4.....100}.\dfrac{3.4.....101}{2.3.4.....100}\)
A=\(\dfrac{1}{100}.\dfrac{101}{2}\)
A=\(\dfrac{101}{200}\)
\(A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{99.101}{100.100}\\ =\dfrac{1}{2}.\dfrac{101}{100}=\dfrac{101}{200}\)
\(B=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)...\left(1-\dfrac{1}{10000}\right)\\ =\dfrac{3}{4}.\dfrac{8}{9}...\dfrac{9999}{10000}\)
(làm như câu a)
Tính các tích sau:
A= 3/4.8/9.15/16...9999/10000
B=(1-1/4).(1-1/9)...(1-1/10000).
C=(1+1/1.3)(1+1/2.4)(1+1/3.15)....(1+1/99.100).
A = \(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\frac{9999}{10000}=\frac{1\cdot3}{2.2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3.5}{4.4}\cdot\cdot\cdot\cdot\frac{99\cdot101}{100\cdot100}=\frac{1}{2}\cdot\frac{101}{100}=\frac{101}{200}\)
B = ( 1- 1/4 )( 1-1/9) ...( 1-1/10000 ) = 3/4 . 8/9 .....9999/100000 ( tương tự A )
(1-1/4)x(1-1/9)x(1-1/16)x.....x(1-1/10000)
Tính nhanh hộ mình nhé
(1-1/4)x(1-1/9)x(1-1/16)x.....x(1-1/10000)
Tính nhanh hộ mình nhé
đáp số cuối cùng là 0 vì 1-1/4 = 0/4 = 0 x cho những số nào khác cũng bằng 0 thôi
\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{10000}\right)\)
\(=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{999}{10000}\)
\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times...\times\frac{99\times101}{100\times100}\)
\(=\frac{1}{2}\times\frac{101}{100}\)
\(=\frac{101}{200}\)
Chu Nguyen Nhan sai rồi nhé 1-1/4 mà bằng 0 à Học lại đê
M=(1- 1/4)×(1-1/9)×(1-1/16) ×........× (1-1/10000)
Tính nhanh giá trị biểu thức
M = \(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}.\right)\left(1-\frac{1}{16}\right)....\left(1-\frac{1}{10000}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{9999}{10000}=\frac{3.8.15...9999}{4.9.16....10000}=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right)....\left(99.101\right)}{\left(2.2\right).\left(3.3\right).\left(4.4\right)....\left(100.100\right)}\)
\(=\frac{\left(1.2.3...99\right).\left(3.4.5..101\right)}{\left(2.3.4...100\right)\left(2.3.4...100\right)}=\frac{1.101}{100.2}=\frac{101}{200}\)
1) Tính
A= 3/4.8/9.15/16...9999/10000
B= (1-1/4).(1-1/9)...(1-1/1000)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{9999}{10000}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)
\(=\frac{1.2.3....99}{2.3.4....100}.\frac{3.4.5....101}{2.3.4...100}\)
\(=\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)
\(B=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).....\left(1-\frac{1}{10000}\right)\)
\(=\frac{3}{4}.\frac{8}{9}....\frac{9999}{10000}=\frac{101}{200}\)
(1-1/4)*(1-1/9)*(1-1/16)*.......*(1-1/10000)=?