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3/4 x 8/9 x 15/16 x ... x 99/100 x 120/121 = 3 x 8 x 15 x 99 x 120/ 4 x 9 x 16 x 100 x 121
= ( 1 x 3 ) x ( 2 x 4 ) x ( 3 x 5 ) x ... x ( 9 x 11 ) x ( 10 x 12 ) / ( 2 x 2 ) x ( 3 x 3 ) x ( 4 x 4 ) x ... x ( 10 x 10 ) x ( 11 x 11 )
= ( 1 x 2 x 3 x ... x 10 ) x ( 3 x 4 x 5 x ... x 12 ) / ( 2 x 3 x ... x 11 ) x ( 2 x 3 x ... x 11 ) = 12/11x2 = 6/11
Câu b
Ta có :x + 3 /1.3 +3/3.5 + 3/5.7+...+3/13.15=2 1/5
X + 2/3.(1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15)1=11/5
X+2/3.(1-1/15)=11/5
X+ 2/3.14/15=11/5
X + 28/45=11/5
X = 11/5 -28/45
X=71/45
Câu a gợi ý
1/2-1/3/1/6=0
1/2- 1/3 - 1/6 ) x (1/2 + 2/3 + 3/4 +4/5 + .......+ 2019 /2020 ) =0
3/4:x=9/10
X = 3/4:9/10
X = 5/6
Bài 2:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
\(\left(4.5-2\cdot x\right):\frac{3}{4}=1\frac{1}{3}\)
\(\left(4.5-2x\right):\frac{3}{4}=\frac{4}{3}\)
\(\left(4.5-2x\right)=\frac{4}{3}\cdot\frac{3}{4}\)
\(4.5-2x=1\)
\(2x=4.5-1\)
\(2x=3.5\)
\(x=3.5:2\)
\(x=1.75\)
(4,5 - 2 x X) : 3/4 = 1 1/3
(4,5 - 2 x X) = 1 1/3 x 3/4
(4,5 - 2 x X) = 1
2 x X = 4,5 - 1
2 x X = 3,5
X = 3,5 : 2
X = 1,75
chúc bạn học giỏi ^_^
tk mk nha !!!
đơn giản :
A=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+........+\(\frac{1}{99.100}\)
A= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)
A=1 - \(\frac{1}{100}\)
A= \(\frac{99}{100}\)
CÓ AI DÙNG HỌC 24 GIỜ KO
A = 1/2 + 1/6 / + 1/ 12 + 1/20 + ......+ 1/(99.100)
A= 1/ ( 1 x 2 ) + 1/ ( 2 x 3 ) + 1 / ( 3 x 4 ) + .....+ 1/ ( 99 x 100 )
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .................+ 1/99 - 1/100
A= 1 - 1/100
A= 99/100
CHÚC BẠN HỌC TỐT
\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\cdot....\cdot\left(1-\frac{1}{2003}\right)\left(1-\frac{1}{2004}\right)\)
\(=\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot....\cdot\frac{2002}{2003}\cdot\frac{2003}{2004}\)
\(=\frac{2\cdot3\cdot4\cdot...\cdot2002\cdot2003}{3\cdot4\cdot5\cdot...\cdot2003\cdot2004}=\frac{1}{1002}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\cdot\cdot\cdot\cdot\cdot\frac{2016}{2017}\)
\(=\frac{1.2........2016}{2.3.............2017}\)
\(=\frac{1}{2017}\)
a) \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(x-\frac{1}{4}\right).....\left(1-\frac{1}{2016}\right).\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{2015}{2016}.\frac{2016}{2017}=\frac{1}{2017}\)