\(P=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+...+\frac{99}{5^{99}}\)
\(5P=1+\frac{2}{5}+\frac{3}{5^2}+...+\frac{99}{5^{98}}\)
\(\Rightarrow4P=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{98}}-\frac{99}{5^{99}}=A-\frac{99}{5^{99}}\)
\(A=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{98}}\)
\(5A=5+1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{97}}\)
\(\Rightarrow4A=5-\frac{1}{5^{98}}< 5\Rightarrow A< \frac{5}{4}\)
\(4P=A-\frac{99}{5^{99}}< A< \frac{5}{4}\Rightarrow P< \frac{5}{16}\)
1. Ta có thể viết số hữu tỉ \(\frac{-5}{16}\) dưới các dạng sau đây :
a) \(\frac{-5}{16}\) là tích của hai số hữu tỉ. Ví dụ : \(\frac{-5}{16}\) = \(\frac{-5}{2}\).\(\frac{1}{8}\)
b) \(\frac{-5}{16}\) là thương của hai số hữu tỉ. Ví dụ: \(\frac{-5}{16}\) = \(\frac{-5}{2}\):8
2. Tính:
a) \(\frac{-3}{4}.\frac{12}{-5}.\)\(\left(-\frac{25}{6}\right)\)
b) (\(-2\)).\(\frac{-38}{21}.\frac{-7}{4}.\left(-\frac{3}{8}\right)\)
c) \(\left(\frac{11}{12}:\frac{33}{16}\right).\frac{3}{5}\)
d) \(\frac{7}{23}.\left[\left(-\frac{8}{6}\right)-\frac{45}{18}\right]\)
3. Tính:
a) \(\left(\frac{-2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
b) \(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)\)
1. Thực hiện phép tính sau một cách hợp lí:
A=\(\frac{\frac{3}{7}-\frac{3}{17}+\frac{3}{37}}{\frac{5}{7}-\frac{5}{17}+\frac{5}{37}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{7}{5}-\frac{7}{4}+\frac{7}{3}-\frac{7}{2}}\)
a)\(1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)
b)\(\frac{3}{7}.19.\frac{1}{3}-\frac{3}{7}.33\frac{1}{3}\)
c)\(15\frac{1}{4}:(\frac{-5}{7})-25\frac{1}{4}:(\frac{-5}{7})\)
bài 1:
a, (-\(2\frac{1}{5}\)).(\(\frac{-9}{11}\)).(-1\(\frac{1}{14}\)).\(\frac{2}{5}\)
b, [\(\frac{5}{3}\)- (-\(\frac{1}{4}\)): 1\(\frac{1}{5}\)]: (\(\frac{5}{8}\)+\(\frac{9}{4}\))
c,-66. (\(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{11}\))+124. -37+ 63. (-123)
d, C= \(\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}-\frac{2}{7}-\frac{2}{13}}\). \(\frac{\frac{1}{3}-0,25+0,2}{1\frac{1}{6}-0,875+0,7}\)+ \(\frac{6}{7}\)
e, D= (\(\frac{1}{4}\)-1). (\(\frac{1}{9}\)-1).(\(\frac{1}{16}\)-1)....(\(\frac{1}{81}\)-1).(\(\frac{1}{100}\)-1)
bài 2:
a, x: (\(\frac{2}{9}\)-\(\frac{1}{5}\))=\(\frac{8}{16}\)
b,(2x-1).(2x+3)=0
c,\(\frac{4-3x}{2x+5}\)=0
d,(x-2). (x+\(\frac{2}{3}\))≥0
e, \(\frac{x-2}{3x+2}\)<0
MỌI NGƯỜI LÀM NHANH GIÚP MÌNH VỚI. MÌNH ĐANG CẦN GẤP TRONG 3H CHIỀU NAY
Tính bằng cách hợp lí nhất :
1/ \(\left(\frac{4}{9}-\frac{5}{11}\right):\frac{3}{10}+\left(\frac{3}{9}-\frac{9}{11}\right):\frac{3}{10}-\left(\frac{2}{9}-\frac{2}{8}\right).\frac{-10}{3}\)
2/ \(\frac{1}{2}.\frac{1}{-3}+\frac{1}{-3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{-5}+\frac{1}{-5}.\frac{1}{6}\)
3/ \(-\frac{7}{4}\left(\frac{33}{12}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)\)
1. x : (\(\frac{2}{9}-\frac{1}{5}\))=\(\frac{8}{16}\)
2. a)\(\frac{x-3}{-2}\)>0
b) \(x^2\)+x >0
c) \(\frac{x+3}{x-5}\)<0
Tính giá trị biểu thức sau:
\(\frac{0,125-\frac{1}{5}+\frac{1}{7}}{0,375-\frac{3}{5}+\frac{3}{7}}\)+\(\frac{\frac{1}{2}+\frac{1}{3}-0,2}{\frac{3}{4}+0,5-\frac{3}{10}}\)
1) Tìm x:
a) \(\frac{11}{12}-\frac{5}{12}.\left(\frac{2}{5}+x\right)=\frac{2}{3}\)
b) \(\frac{3}{4}+\frac{1}{4}:x=\frac{2}{5}\)
c) 2x.(x-\(\frac{1}{7}\))=0
d) (x + 1) . (x - 2) < 0
e) (x - 2) . ( x + \(\frac{2}{3}\) ) >0
\(\frac{1}{2}x-\frac{7}{8}=\frac{5}{6}x-\frac{1}{16}\)
