Cho I; \(\dfrac{11}{3}\)+\(\dfrac{17}{3^2}\)+\(\dfrac{17}{3^2}\)+...+ \(\dfrac{302}{3^{100}}\)
CMR; I bé hơn 7
*Rút gọn
1) G=\(\dfrac{2}{3}+\dfrac{2}{3^3}+\dfrac{2}{3^5}+...+\dfrac{2}{3^{99}}\)
2) H=\(\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{16}}+...-\dfrac{1}{2^{58}}\)
3) E=\(\dfrac{-1}{3}+\left(\dfrac{-1}{3}\right)^2+\left(\dfrac{-1}{3}\right)^3+...+\left(\dfrac{-1}{100}\right)^{100}\)
Tính biểu thức A=\(\dfrac{\dfrac{3}{4}-\dfrac{3}{11}+\dfrac{3}{13}}{\dfrac{5}{7}-\dfrac{5}{11}+\dfrac{5}{13}}+\dfrac{\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}}{\dfrac{5}{4}-\dfrac{5}{6}+\dfrac{5}{8}}\)
5. \(3-1\dfrac{1}{2}-x+\dfrac{5}{4}=2-\left|1\dfrac{1}{8}-\dfrac{5}{12}\right|\) 6. \(3\dfrac{1}{14}-5\dfrac{1}{3}-\dfrac{4}{7}+\dfrac{11}{21}=-\dfrac{1}{2}\) 7. \(\dfrac{11}{-40}+\dfrac{4}{5}-\left|\dfrac{3}{4}-1\dfrac{5}{12}\right|=\dfrac{3}{20}-X\)
5. \(3-1\dfrac{1}{2}-x+\dfrac{5}{4}=2-\left|1\dfrac{1}{8}-\dfrac{5}{12}\right|\) 6. \(3\dfrac{1}{14}-5\dfrac{1}{3}-\dfrac{4}{7}+\dfrac{11}{21}=x-\dfrac{1}{2}\) 7. \(\dfrac{11}{-40}+\dfrac{4}{5}-\left|\dfrac{3}{4}-1\dfrac{5}{12}\right|=\dfrac{3}{20}-x\)
8) \(\dfrac{17}{-26}.\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}.\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}.\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
1, Tìm các số hữu tỉ:
a) Có dạng \(\dfrac{12}{b}\) sao cho \(\dfrac{-8}{19}< \dfrac{12}{b}< \dfrac{-2}{5}\)
b) Có dạng \(\dfrac{9}{b}\) sao cho \(\dfrac{8}{11}< \dfrac{9}{b}< \dfrac{12}{13}\)
2, Tính:
M=\(54-\dfrac{1}{2}\left(1+2\right)-\dfrac{1}{3}\left(1+2+3\right)-\dfrac{1}{4}\left(1+2+3+4\right)-...\dfrac{1}{12}\left(1+2+3+...+12\right)\)
3, Rút gọn các biểu thức sau:
a) A= \(\dfrac{9^9+27^7}{9^6+243^3}\)
b) B= \(\dfrac{\left(\dfrac{2}{3}\right)^5.\left(\dfrac{-27}{8}\right)^2.729}{\left(\dfrac{3}{2}\right)^4.216}\)
4, Cho a,b,c là các số nguyên dương sao cho mỗi số nhỏ hơn tổng của hai số kia. Chứng minh rằng \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}< 2\)
5, Cho A= \(\dfrac{1001}{1000^2+1}+\dfrac{1001}{1000^2+2}+...+\dfrac{1001}{1000^2+1000}\)
Chứng minh rằng 1<A2 < 4
Câu 1. 1- (x + \(\dfrac{1}{3}\) )\(^2\) = \(\dfrac{5}{9}\)
Câu 2. 15 :( \(\dfrac{4}{9}\))\(^2\) . (\(\dfrac{8}{27}\))\(^2\) : (\(\dfrac{2}{3}\))\(^9\)
Tính :
A = \(\dfrac{\dfrac{3}{7}-\dfrac{3}{11}+\dfrac{3}{13}}{\dfrac{5}{7}-\dfrac{5}{11}+\dfrac{5}{13}}+\dfrac{\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}}{\dfrac{5}{4}-\dfrac{5}{6}+\dfrac{5}{3}}\)
