bài 1 tính
( 1 - 1/4) x (1 -1/9) x ( 1-1/16) x (1-1/25)
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29 tháng 1
\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)
\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)
\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)
15 tháng 10 2021
a: \(2x\left(x^2-3x+1\right)=2x^3-6x^2+2x\)
b: \(\left(x+2\right)^2-x^2=4x+4\)
c: \(\left(x+3\right)\left(x^2-3x+9\right)-x^3=27\)
11 tháng 4 2017
\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}=\frac{3.8.15.24.35}{4.9.16.25.36}=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}\)
\(=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{2.2}=\frac{7}{4}\)
30 tháng 7 2015
c)x:25/8-3/4=9/4
x:25/8=9/4+3/4
x:25/8=3
x=3 nhân 25/8
x=75/8
tất cả các bài có người làm rồi li-ke cho mình nha
11 tháng 7 2023
=(1-1/3)(1-1/4)(1-1/5)*...*(1-1/50)(1+1/3)(1+1/4)*...*(1+1/50)
=2/3*3/4*...*49/50*4/3*5/4*...*51/50
=2/50*51/3=17*1/25=17/25
H9
HT.Phong (9A5)
CTVHS
11 tháng 7 2023
\(\left(1-\dfrac{1}{9}\right)\cdot\left(1-\dfrac{1}{16}\right)\cdot\left(1-\dfrac{1}{25}\right)\cdot...\cdot\left(1-\dfrac{1}{2500}\right)\)
\(=\left(\dfrac{9}{9}-\dfrac{1}{9}\right)\cdot\left(\dfrac{16}{16}-\dfrac{1}{16}\right)\cdot...\cdot\left(\dfrac{2500}{2500}-\dfrac{1}{2500}\right)\)
\(=\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdot...\cdot\dfrac{2499}{2500}\)
\(=\dfrac{8\cdot15\cdot24\cdot...\cdot2499}{9\cdot16\cdot25\cdot...\cdot2500}\)
\(=\dfrac{\left(2\cdot4\right)\cdot\left(3\cdot5\right)\cdot\left(4\cdot6\right)\cdot....\cdot\left(49\cdot51\right)}{\left(3\cdot3\right)\cdot\left(4\cdot4\right)\cdot\left(5\cdot5\right)\cdot...\cdot\left(50\cdot50\right)}\)
\(=\dfrac{\left(2\cdot3\cdot4\cdot5\cdot...\cdot49\right)\left(4\cdot5\cdot6\cdot...\cdot51\right)}{\left(2\cdot3\cdot4\cdot...\cdot50\right)\left(2\cdot3\cdot4\cdot...\cdot50\right)}\)
\(=\dfrac{1\cdot51}{50\cdot2}\)
\(=\dfrac{51}{100}\)
2 tháng 7 2018
b, 3/5 + 4/7 + 2/8 + 10/25 + 9/21 + 28/16
= 3/5 + 4/7 + 2/8 + 2/5 + 3/7 + 14/8
= (3/5 + 2/5) + ( 4/7 + 3/7) + ( 2/8 + 14/8)
= 1 + 1 + 7/4
= 2 + 7/4 = 15/4
c , 8/7 + 7/6 + 5/8 + 10/12 + 24/28 + 6/16
= c , 8/7 + 7/6 + 5/8 + 5/6 + 6/7 + 1/2
= (8/7 + 6/7) + (7/6 + 5/6) + 5/8 + 1/2
= 14/7 + 12/6 + 5/8 + 1/2
= 2 + 2 + 5/8 + 1/2
= 4 + 9/8 = 41/8
MD
2
NN
13 tháng 7 2016
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]
\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}\)
\(=\frac{3x8x15x24}{4x9x16x25}\)
\(=\frac{3x2x4x3x5x4x2x3}{2x2x3x3x4x4x5x5}\)(chỗ này rút gọn đi)
\(=\frac{3}{5}\)