chứng minh rằng: \({1\over2}+{1\over3}+{1\over4}+...+{1\over63}>2\)
a) \({ {1} \over 3}x + { {2}\over5}(x-1) = 0\)
b)\(|x + { {3} \over 7}|={ {1}\over4} - { {1}\over5}\)
Chứng minh với mọi số nguyên dương n ta có
\(x = {1\over2}.{3\over4}.{5\over6}...{2n+1\over2n+2}<{1\over sqrt {3n++4}}\)
\({2x{}\over3} = {2y{}\over4} = {4z{}\over5}\) và x+y+z=49
Thu gon biểu thức
\(A=(-{1\over2}x^3y^2z)+{3\over4}x^3y^2z-x^3y^2z\)
\(B=(-xy^2)^3x^3+(0,5xy)^3x^3y^3-{x^6y^6\over2}\)
thu gọn biểu thức .........(cái j zợ)................
Cho x,y,z >0 thỏa mãn \( {1 \over x}+ {1\over y} + {1\over z}=3\)
Chứng minh rằng \({x\over x^4+1+2xy}+{y\over y^4+1+2yz} + {z\over z^4+1+2zx}<= {3\over4}\)
Bài 1:Tính
a) A= (-3)+(-6)+(-9)+...+(-90)
b) \(B = {3\over 5.7}+{3\over 7.9}+{3\over 9.11}+...+{3\over97.99}\)
Bài 2:
a)So sánh: \( A = {15^30-1 \over 15^29-1} và B= {15^31-1\over 15^30-1}\)
b)Tìm chữ số a, b biết: 4a5b \(⋮\)4, 4a5b : 3 dư2
Bài 3:Tính A/B:
\(A = {1\over2}+{1\over3}+{1\over4}+...+{1\over308}+{1\over309} \)
\(B = { 308\over1}+{ 307\over 2}+{ 306\over 3}+...+{ 3\over306}+{ 2\over 307}+{ 3\over 308}\)
TÌM X
\(1\dfrac{1}{3}:0,8=\dfrac{2}{3}:0,1X\)
NHANH LÊN \(1\dfrac{1}{3}:0,8=\dfrac{2}{3}:0,1X\)
\(1\dfrac{1}{3}:0,8=\dfrac{2}{3}:\left(0,1\right).x\)
\(\Rightarrow\dfrac{4}{3}:\dfrac{4}{5}=\dfrac{2}{3}:\dfrac{1}{10}.x\)
\(\Rightarrow\dfrac{4}{3}.\dfrac{5}{4}=\dfrac{2}{3}.10x\)
\(\Rightarrow\dfrac{5}{3}=\dfrac{2}{3}.10x\)
\(\Rightarrow10x=\dfrac{5}{3}:\dfrac{2}{3}\)
\(\Rightarrow10x=\dfrac{5}{2}\)
\(\Rightarrow x=\dfrac{5}{2}:10=\dfrac{1}{4}\)
Vậy \(x=\dfrac{1}{4}\)
\(1\dfrac{1}{3}:0,8=\dfrac{2}{3}:0,1x\Rightarrow\dfrac{4}{3}:\dfrac{3}{5}=\dfrac{2}{3}:\dfrac{1}{10}x\)
\(\Rightarrow\dfrac{4}{3}.\dfrac{5}{3}=\dfrac{2}{3}.10x\Rightarrow\dfrac{20}{9}=\dfrac{20}{3}x\Rightarrow x=\dfrac{1}{3}\)
Vậy...................................................
1/2 × 2/5 × 1/5 × 0,8 × 0,25 × 0,125
\(\frac{1}{2}x\frac{2}{5}x\frac{1}{5}x0,8x0,25x0,125\)
=\(\frac{1}{2}x\frac{2}{5}x\frac{1}{5}x\frac{4}{5}x\frac{1}{4}x\frac{1}{8}\)
=\(\frac{1x2x1x4x1x1}{2x5x5x5x4x8}\)
=\(\frac{1x1x1x1x1x1}{1x5x5x5x1x8}\)
=\(\frac{1}{1000}\)
\(\frac{1}{2}\times\frac{2}{5}\times\frac{1}{5}\times0,8\times0,25\times0,125\)
\(=0,5\times0,4\times0,2\times0,8\times0,25\times0,125\)
\(=\left(0,5\times0,2\right)\times\left(0,4\times0,25\right)\times\left(0,8\times0,125\right)\)
\(=0,1\times0,1\times0,1\)
\(=0,001\)