Tính bằng cách thuận tiện :
\( { \ \ {1} \over 1*3} + { \ \ {1} \over 3*5} + { \ \ {1} \over 5*7} + ....+ { \ \ {1} \over 45*47}\)
Những câu hỏi liên quan
Chứng minh :
\(x = {1 \over \sqrt{1}+\sqrt{2}}+{1 \over \sqrt{3}+\sqrt{4}}+{1 \over \sqrt{5}+\sqrt{6}}+...+{1 \over \sqrt{47}+\sqrt{48}}>3\)
a. 2016 : [ 25 - (3x + 2)] 32 . 7b, 52x - 3 - 2 . 52 52 . 3c,{-3 over 4x}-{20 over 11.13}-{20 over 13.15}-{20 over 15.17}-.....-{20 over 53.55}{3 over 11}d,{x over 6}+{x over 10}+{x over 15}+{x over 21}+{x over 28}+{x over 36}+{x over 45}+{x over 55}+{x over 66}+{x over 78}{220 over 39}e, x+(x-1)+(x-2)+(x-3)+......+(x-2016) 2033136
Đọc tiếp
a. 2016 : [ 25 - (3x + 2)] = 32 . 7
b, 52x - 3 - 2 . 52 = 52 . 3
c,\({-3 \over 4x}-{20 \over 11.13}-{20 \over 13.15}-{20 \over 15.17}-.....-{20 \over 53.55}={3 \over 11}\)
d,\({x \over 6}+{x \over 10}+{x \over 15}+{x \over 21}+{x \over 28}+{x \over 36}+{x \over 45}+{x \over 55}+{x \over 66}+{x \over 78}={220 \over 39}\)
e, x+(x-1)+(x-2)+(x-3)+......+(x-2016) = 2033136
1.A {3 over 5}.{2017 over 2016} - {3 over 5}- {1 over 2016} + {2 over 5}B ({12 over 199}+ {23 over 200} - {34 over 201}).({1over 2} - {1 over 3}-{1 over 6})C 2{1 over 3}+{11 over 5}: 33-{1 over 50}.(-5)2D {4^5 . 9^4 - 10 . 6^9 over 2^10 . 3^8 + 6^8 . 28}E ( -1).(-1)2.(-1)3.(-1)4......(-1)20142.A {5over2.4} + {5over4.6} + {5over6.8} + .....+ {5over48.50}B{1over3.6} + {1over6.9} + {1over9.12} +.....+{1over30.33}
Đọc tiếp
1.
\(A = {3 \over 5}.{2017 \over 2016} - {3 \over 5}- {1 \over 2016} + {2 \over 5}\)
\(B = ({12 \over 199}+ {23 \over 200} - {34 \over 201}).({1\over 2} - {1 \over 3}-{1 \over 6})\)
\(C= 2{1 \over 3}+{11 \over 5}: 33-{1 \over 50}.\)(-5)2
\(D = {4^5 . 9^4 - 10 . 6^9 \over 2^10 . 3^8 + 6^8 . 28}\)
E =( -1).(-1)2.(-1)3.(-1)4......(-1)2014
2.
\(A= {5\over2.4} + {5\over4.6} + {5\over6.8} + .....+ {5\over48.50}\)
\(B={1\over3.6} + {1\over6.9} + {1\over9.12} +.....+{1\over30.33}\)
Giải các phương trình sau : a, {8 over x-8} + { 11over x-11} {9 over x-9} +{10 over x-10}b, {x over x-3} - {x over x-5} { x over x-4} - { xover x-6}c, { 4over x^2 - 3x + 2 } - { 3 over 2x^2 - 6x +1 } +1 0d, {1over x-1} + {2over x-2} + {3 over x-3} {6 over x-6}e, {2over 2x+1} - {3 over 2x-1} {4over 4x^2 -1}f, { 2xover x +1 } + { 18 over x^2 +2x-3} {2x-5 over x+3}g, {1 over x-1} + { 2x^2 -5 over x^3 -1 } { 4 over x^2 +x+1}
Đọc tiếp
Giải các phương trình sau :
a, \({8 \over x-8} + { 11\over x-11} = {9 \over x-9} +{10 \over x-10}\)
b, \({x \over x-3} - {x \over x-5} = { x \over x-4} - { x\over x-6}\)
c, \({ 4\over x^2 - 3x + 2 } - { 3 \over 2x^2 - 6x +1 } +1 =0\)
d, \({1\over x-1} + {2\over x-2} + {3 \over x-3} = {6 \over x-6}\)
e, \({2\over 2x+1} - {3 \over 2x-1} = {4\over 4x^2 -1}\)
f, \({ 2x\over x +1 } + { 18 \over x^2 +2x-3} = {2x-5 \over x+3}\)
g, \({1 \over x-1} + { 2x^2 -5 \over x^3 -1 } = { 4 \over x^2 +x+1}\)
a, 8/x-8 + 11/x-11 = 9/x-9 + 10/ x-10
b, x/x-3 - x/x-5 = x/x-4 - x/x-6
c, 4/x^2-3x+2 - 3/2x^2-6x+1 +1 = 0
d, 1/x-1 + 2/ x-2 + 3/x-3 = 6/x-6
e, 2/2x+1 - 3/2x-1 = 4/4x^2-1
f, 2x/x+1 + 18/x^2+2x-3 = 2x-5 /x+3
g, 1/x-1 + 2x^2 -5/x^3 -1 = 4/ x^2 +x+1
Bài 1:So sánh
A=10/22017+10/22018 và B=11/22017+92018
Bài 2
\(A = {1 \over 2}.{3\over 4}.{4\over 5}.{5\over 6}.{7\over 8}. ... .{99\over 100}\) và \(x = {2\over 3}.{4\over 5}.{6\over 7}.{8\over 9}. ... .{100\over 101}\)
a,So sánh
b,Chứng minh A<1/16
Tính giá trị biểu thức:
\(25*({-1\over 5})^3+ {1\over 5}- {1\over 2}\)
Bài 1: Rút gọn
1) x^2-y^2 over 6x^2y^2
÷ x+y over 12xy
2) 5x over 2x+1
÷ 3x(x-1) over 4x^2-1
3)( 2x-1over 2x+1
-2x-1over 2x+1
) ÷ 4x over 10x-5
4) 2over 9x^2+6x+1
- 3x over 9x^2-1
5) (5over x^2+2x+1 +2x over x^2-1
) ÷ 2x^2+7x-5 over 3x-3
6) (3over x-3 + 2x over x^2-9
+ xover x+3
) ÷ 2xover x+3
7) (3over x^2-9
+1over x^2+3x
-1over x^2-3x
) ÷ x-2over 2x^2+6x
Đọc tiếp
Bài 1: Rút gọn
1) \(x^2-y^2 \over 6x^2y^2 \)÷ \(x+y \over 12xy\)
2) \(5x \over 2x+1 \) ÷ \(3x(x-1) \over 4x^2-1\)
3)( \(2x-1\over 2x+1 \)-\(2x-1\over 2x+1 \)) ÷ \(4x \over 10x-5 \)
4) \(2\over 9x^2+6x+1 \)- \(3x \over 9x^2-1 \)
5) (\(5\over x^2+2x+1 \)+\(2x \over x^2-1 \)) ÷ \(2x^2+7x-5 \over 3x-3\)
6) (\(3\over x-3 \)+ \(2x \over x^2-9 \) + \(x\over x+3 \)) ÷ \(2x\over x+3\)
7) (\(3\over x^2-9 \)+\(1\over x^2+3x \)-\(1\over x^2-3x \)) ÷ \(x-2\over 2x^2+6x\)
1)
ĐK: \(x,y\neq 0\); \(x+y\neq 0\)
\(\frac{x^2-y^2}{6x^2y^2}: \frac{x+y}{12xy}\)
\(=\frac{x^2-y^2}{6x^2y^2}. \frac{12xy}{x+y}=\frac{(x-y)(x+y).12xy}{6x^2y^2(x+y)}=\frac{2(x-y)}{xy}\)
2) ĐK: \(x\neq \frac{\pm 1}{2}; 0; 1\)
\(\frac{5x}{2x+1}: \frac{3x(x-1)}{4x^2-1}=\frac{5x}{2x+1}.\frac{4x^2-1}{3x(x-1)}\)
\(=\frac{5x(2x-1)(2x+1)}{(2x+1).3x(x-1)}=\frac{5(2x-1)}{3(x-1)}\)
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3) ĐK: \(x\neq \frac{\pm 1}{2}; 0\)
\(\left(\frac{2x-1}{2x+1}-\frac{2x-1}{2x+1}\right): \frac{4x}{10x-5}=0: \frac{4x}{10x-5}=0\)
4) ĐK: \(x\neq \frac{\pm 1}{3}\)
\(\frac{2}{9x^2+6x+1}-\frac{3x}{9x^2-1}=\frac{2}{(3x+1)^2}-\frac{3x}{(3x-1)(3x+1)}\)
\(=\frac{2(3x-1)}{(3x+1)^2(3x-1)}-\frac{3x(3x+1)}{(3x-1)(3x+1)^2}\)
\(=\frac{6x-2-9x^2-3x}{(3x+1)^2(3x-1)}=\frac{-9x^2+3x-2}{(3x-1)(3x+1)^2}\)
5) ĐK: \(x\neq \pm 1; \frac{-7\pm \sqrt{89}}{4}\)
\(\left(\frac{5}{x^2+2x+1}+\frac{2x}{x^2-1}\right): \frac{2x^2+7x-5}{3x-3}\)
\(=\left(\frac{5}{(x+1)^2}+\frac{2x}{(x-1)(x+1)}\right). \frac{3(x-1)}{2x^2+7x-5}\)
\(=\frac{5(x-1)+2x(x+1)}{(x-1)(x+1)^2}. \frac{3(x-1)}{2x^2+7x-5}=\frac{2x^2+7x-5}{(x+1)^2(x-1)}.\frac{3(x-1)}{2x^2+7x-5}\)
\(=\frac{3}{(x+1)^2}\)
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6) ĐK: \(x\neq \pm 3\); 0
\(\left(\frac{3}{x-3}+\frac{2x}{x^2-9}+\frac{x}{x+3}\right): \frac{2x}{x+3}\)
\(=\left(\frac{3(x+3)}{(x-3)(x+3)}+\frac{2x}{(x-3)(x+3)}+\frac{x(x-3)}{(x+3)(x-3)}\right). \frac{x+3}{2x}\)
\(=\frac{3(x+3)+2x+x(x-3)}{(x-3)(x+3)}.\frac{x+3}{2x}\)
\(\frac{(x^2+2x+9)(x+3)}{(x-3)(x+3).2x}=\frac{x^2+2x+9}{2x(x-3)}\)
7) ĐK: \(x\neq 2; \pm 3;0\)
\(\left(\frac{3}{x^2-9}+\frac{1}{x^2+3x}-\frac{1}{x^2-3x}\right): \frac{x-2}{2x^2+6x}\)
\(=\left(\frac{3x}{x(x-3)(x+3)}+\frac{x-3}{x(x-3)(x+3)}-\frac{x+3}{(x+3)x(x-3)}\right).\frac{2x(x+3)}{x-2}\)
\(=\frac{3x+x-3-(x+3)}{x(x-3)(x+3)}.\frac{2x(x+3)}{x-2}\)
\(=\frac{3x-6}{x(x-3)(x+3)}.\frac{2x(x+3)}{x-2}=\frac{3(x-2).2x(x+3)}{x(x-3)(x+3)(x-2)}=\frac{6}{x-3}\)
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1.Tìm x,biết:
a)\(x+4 \over 2018\)+\(x+3 \over 2019\)+\(x+2 \over 2020\)=-1
b)\(3 \over 5\)+\(2 \over 5\):x=1
c)3/2x-1/-2=4
Tìm x,y,n thuộc Z biết :1 . {3 over n + 1} thuộc Z2 . {-2 over n-1}thuộc Z 3 . {3 over y} {2 over 5}4 . {n over n + 1}thuộc Z5 . {- 6 over 30} {x over - 20}{3 over y} {z over 5}
Đọc tiếp
Tìm x,y,n thuộc Z biết :
1 . \({3 \over n + 1} \) thuộc Z
2 . \({-2 \over n-1}\)thuộc Z
3 . \({3 \over y}\)= \({2 \over 5}\)
4 . \({n \over n + 1}\)thuộc Z
5 . \({- 6 \over 30}\)= \({x \over - 20}\)\(=\)\({3 \over y} = {z \over 5}\)