(1-1/2)*(1-1/3)*...........*(1-1/x)
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\(A=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)\left(1-\frac{1}{1+2+3+4}\right)...\left(1-\frac{1}{1+2+3+4+...+2018}\right)\)
\(A=\frac{2}{1+2}\cdot\frac{2+3}{1+2+3}\cdot\frac{2+3+4}{1+2+3+4}\cdot...\cdot\frac{2+3+4+5+...+2018}{1+2+3+4+5+...+2018}\)
Đến chỗ này đố ai tính được ?!!?!
gạch các số của tử số và các số của mẫu số giống nhau
ví dụ như bạn nói:
\(\dfrac{2+3+4+5+...+2018}{1+2+3+4+5+...+2018} =1\)
1) ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
Ta có: \(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{4}{x^2-1}\)
\(\Leftrightarrow\dfrac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\dfrac{4}{\left(x-1\right)\left(x+1\right)}\)
Suy ra: \(x^2+2x+1-\left(x^2-2x+1\right)=4\)
\(\Leftrightarrow x^2+2x+1-x^2+2x-1=4\)
\(\Leftrightarrow4x=4\)
hay x=1(loại)
Vậy: \(S=\varnothing\)
2) ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
Ta có: \(\dfrac{x+2}{x-2}+\dfrac{x}{x+2}=2\)
\(\Leftrightarrow\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2\left(x^2-4\right)}{\left(x-2\right)\left(x+2\right)}\)
Suy ra: \(x^2+4x+4+x^2-2x=2x^2-8\)
\(\Leftrightarrow2x^2+2x+4-2x^2-8=0\)
\(\Leftrightarrow2x-4=0\)
\(\Leftrightarrow2x=4\)
hay x=2(loại)
Vậy: \(S=\varnothing\)
a) 3 3/4 . x = 1 1/2
<=> 15/4 . x = 3/2
<=> x = 3/4 . 4/15
<=> x = 1/5
Vậy x = 1/5
b) 1 1/4 x + 1 1/2 = 1 1/4
<=> 5/4 . x + 3/2 = 5/4
<=> 5/4 . x = 5/4 - 3/2
<=> 5/4 . x = -1/4
<=> x = -1/4 . 4/5
<=> x = -1/5
Vậy x = -1/5
c) ( 3 1/3 - 1 1/2 x ) : 5/6 = 1 1/2
<=> ( 10/3 - 3/2 x ) : 5/6 = 3/2
<=> 10/3 - 3/2 x = 3/2 . 5/6
<=> 10/3 - 3/2 x = 5/4
<=> 3/2 . x = 10/3 - 5/4
<=> 3/2 . x = 25/12
<=> x = 25/12 . 2/3
<=> x = 25/18
Vậy x = 25/18
d) ( 3/7 x - 1 ) : 4 = -1/28
<=> 3/7 . x - 1 = -1/28 . 1/4
<=> 3/7 . x - 1 = -1/112
<=> 3/7 . x = -1/112 + 1
<=> 3/7 . x = 111/112
<=> x = 111/112 . 7/3
<=> x = 37/16
Vậy x = 37/16
e) | x - 3/4 | = 1
<=> x - 3/4 = 1
hoặc x - 3/4 = -1
<=> x = 1 + 3/4
hoặc x = -1 + 3/4
<=> x = 7/4
hoặc x = -1/4
Vậy x = 7/4 ; x = -1/4
f) | 2/3 . x + 1/3 | = 5/6
<=> 2/3 . x + 1/3 = 5/6
hoặc 2/3 . x + 1/3 = -5/6
<=> 2/3 . x = 5/6 - 1/3
hoặc 2/3 . x = -5/6 - 1/3
<=> 2/3 . x = 1/2
hoặc 2/3 . x = -7/6
<=> x = 1/2 . 3/2
hoặc x = -7/6 . 3/2
<=> x = 3/4
hoặc x = -7/4
Vậy x = 3/4 ; x = -7/4
\(\frac{1-x}{1+x}+3=\frac{2x+3}{x+1}\left(ĐKXĐ:x\ne-1\right)\)
\(\Leftrightarrow\frac{1-x}{x+1}+\frac{3\left(x+1\right)}{x+1}=\frac{2x+3}{x+1}\)
\(\Leftrightarrow\frac{1-x+3\left(x+1\right)}{x+1}=\frac{2x+3}{x+1}\)
\(\Rightarrow1-x+3\left(x+1\right)=2x+3\)
\(\Leftrightarrow1-x+3x+3=2x+3\)
\(\Leftrightarrow2x+4=2x+3\)
\(\Leftrightarrow0x=-1\)(vô nghiệm)
Vậy phương trình vô nghiệm.
\(\frac{\left(x+2\right)^2}{2x-3}-1=\frac{x^2-10}{2x-3}\left(ĐKXĐ:x\ne\frac{3}{2}\right)\)
\(\Leftrightarrow\frac{x^2+4x+4}{2x-3}-\frac{2x-3}{2x-3}=\frac{x^2-10}{2x-3}\)
\(\Leftrightarrow\frac{x^2+4x+4-2x+3}{2x-3}=\frac{x^2-10}{2x-3}\)
\(\Rightarrow x^2+4x+4-2x+3=x^2-10\)
\(\Leftrightarrow2x+7=-10\)
\(\Leftrightarrow2x=-17\)
\(\Leftrightarrow x=\frac{-17}{2}\)(thỏa mãn ĐKXĐ)
Vậy phương trình có nghiệm duy nhất : \(x=\frac{-17}{2}\)
\(a)\) \(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)
\(S=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)
\(3S=3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)
\(3S-S=\left(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\right)\)
\(2S=3+\frac{1}{3^7}\)
\(2S=\frac{3^8+1}{3^7}\)
\(S=\frac{3^8+1}{3^7}.\frac{1}{2}\)
\(S=\frac{3^8+1}{2.3^7}\)
Vậy \(S=\frac{3^8+1}{2.3^7}\)
Chúc bạn học tốt ~
\(A=2x^3+3x^2-3-5x^2-5x=2x^3-2x^2-5x-3\\ B=125-150x+60x^2-8x^3-25+9x^2=-8x^3+69x^2-150x+100\\ C=\left(3x+1-2x+1\right)\left(3x+1+2x-1\right)=5x\left(x+2\right)=5x^2+10x\\ D=\left(2x+1-3+x\right)^2=\left(3x-2\right)^2=9x^2-12x+4\\ E=x^3-6x^2+12x-8-x^3+x+6x^2-18x=-5x-8\\ F=x^3-3x^2+3x-1-3+3x^2-x^3+1-3x=-3\)
a: =>x-2/5=3/4:1/3=3/4*3=9/4
=>x=9/4+2/5=45/20+8/20=53/20
b: =>x-2/3=7/3:4/5=7/3*5/4=35/12
=>x=35/12+2/3=43/12
c: 1/3(x-2/5)=4/5
=>x-2/5=4/5*3=12/5
=>x=12/5+2/5=14/5
d: =>2/3x-1/3-1/4x+1/10=7/3
=>5/12x-7/30=7/3
=>5/12x=7/3+7/30=77/30
=>x=77/30:5/12=154/25
e: \(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)
=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)
=>x=19/7:23/28=76/23
f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5
=>13/12x=1/5+3/2+4/3+5/4=257/60
=>x=257/65
i: =>x^2-2/5x-x^2-2x+11/4=4/3
=>-12/5x=4/3-11/4=-17/12
=>x=17/12:12/5=85/144
Chị sẽ giúp em nốt mấy bài này, em còn nhận ra chị ko vậy?
\(A=\frac{2}{1x2}+\frac{2}{2x3}+\frac{2}{3x4}+...+\frac{2}{99x101}\)
\(A=2x\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{99x101}\right)\)
\(A=2x\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(A=2x\left(1-\frac{1}{101}\right)=2x\frac{100}{101}=\frac{200}{101}\)
------------------------------
\(B=\left(1+\frac{1}{2}\right)x\left(1+\frac{1}{3}\right)x\left(1+\frac{1}{4}\right)x...x\left(1+\frac{1}{2016}\right)\)
\(B=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x...x\frac{2017}{2016}\) (rút gọn từ trên tử xuống dưới mẫu nhé)
\(B=\frac{2017}{2}\)
-------------------------------
\(C=\frac{3}{1x4}+\frac{3}{4x7}+\frac{3}{7x10}+...+\frac{3}{64x67}\)
\(C=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{64}-\frac{1}{67}\)
\(C=1-\frac{1}{67}=\frac{67}{67}-\frac{1}{67}=\frac{66}{67}\)
--------------------------------
\(D=\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{20}\right)\)
\(D=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{19}{20}\)(chỗ này cũng rút gọn từ trên tử xuống dưới mẫu)
\(D=\frac{1}{20}\)
1.\(\dfrac{-1}{4}\) \(-\) x \(=\dfrac{-3}{2}\)
\(\Leftrightarrow\) x \(\dfrac{-3}{2}-\dfrac{-1}{4}\)
\(\Leftrightarrow\) x \(=\dfrac{-5}{4}\)
1. -1/4 - x = -3/2
x = -1/4 - -3/2
x = -1/4 - -6/4
x = 5/4
2. 3/5 . (x - 1/2) : 3/5 - 1/3 = -1/2
3/5 . (x - 1/2) : 3/5 = -1/2 + 1/3
3/5 . (x - 1/2) : 3/5 = -3/6 + 2/6
3/5 . (x - 1/2) : 3/5 = -1/6
3/5 . (x - 1/2) = -1/6 . 3/5
3/5 . (x - 1/2) = -1/10
x - 1/2 = -1/10 : 3/5
x - 1/2 = -1/6
x = -1/6 + 1/2
x = -1/6 + 3/6
x = 2/6
x = 1/3
Mấy câu sau bn tự làm nha!