Tính :
( 1 - 1/4 ) x ( 1 - 1/9) x ( 1 - 1/16) x ( 1 - 1/25 ) x ( 1 - 1/36)
Lê Mạnh Tiến Đạt giúp mk nhé
Tính ; ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16 ) x ( 1-1/25 ) x ( 1 - 1/36 )
Đỗ Nguyễn Đức Hoàng giải hộ mk nhé!
\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}=\frac{3.8.15.24.35}{4.9.16.25.36}=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}\)
\(=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{2.2}=\frac{7}{4}\)
\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)
\(=\)\(\frac{3}{4}\) 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
Cho S = 3/4 + 8/9 + 15/16 + 24/25 + 35/36 + ....... + (x2-1)/x2
Chứng minh rằng S ko phải là 1 số nguyên
Giúp mk nhé. Ai nhanh mk tk cho. Tks
S=1-1/4+1-1/9+...+1-1/x2
S=(1+1+1+...+1)-(1/4+1/9+...+1/x2)
Có (1/4+1/9+...+1/x2)<1/(1.2)+1/(2.3)+...+1/(x-1)x=1-1/x<1
=> (1/4+1/9+...+1/x2) ko là số nguyên
=>S ko là số nguyên
( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16 ) x ( 1 - 1/25 ) x ( 1 - 1/36 )
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]
(1-1/4)x(1-1/9)x(1-1/16)x(1-1/25)x(1-1/36)=
\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)
\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)
\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)
\(=\)\(\text{}\text{}\text{}\text{}\text{}\text{}\frac{\text{}\text{}\text{}\text{}\text{}\text{}3\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times7}{4\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times8\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times6}\)
\(=\)\(\frac{7\text{}\text{}\text{}\times4}{8\times6}\)
\(=\)\(\frac{7\times4}{4\times2\times6}\)
\(=\)\(\frac{7}{2\times6}\)
\(=\)\(\frac{7}{12}\)
(1-1/4)x(1-1/9)x(1-1/16)x(1-1/25)x(1-1/36)
Tính nhanh:
A = ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16 ) x ( 1 - 1/25 ) x.....x ( 1 - 1/9801 )
Giúp mik với ạ! Cảm ơn!
\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)
\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)
\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)
tinh nhanh
K = [ 1-1/4 ] x [ 1-1/9 ] x [ 1-1/16 ] x [ 1-1/25 ] x [ 1-1/36 ]
K = ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16 ) x ( 1 - 1/25 ) x ( 1 - 1/36 )
\(K=\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)
\(K=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x\frac{35}{36}\)
tự rút gọn
thôi tui làm nốt cho
...
\(K=\frac{1x3}{2x2}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x\frac{4x6}{5x5}x\frac{5x7}{6x6}\)
\(K=\frac{7}{2}\)
Câu 10. Cho (1 − 1/4) x (1 − 1/9) x (1 − 1/26 ) x (1 − 1/25 ) x (1 − 1/36 ) x (1 − 1/49 ) x (1 − 1/64 ) = , biết là phân số tối giản. Tính = + . A. = 28 B. = 25 C. = 30 D. = 36 mik can gap
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