Đặt \(A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\)
\(\Rightarrow5A=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{99}}\)
\(\Rightarrow5A-A=\left(1-\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{99}}\right)-\left(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\right)\)
\(4A=1-\frac{1}{5^{100}}\)
\(\Rightarrow A=\frac{1-\frac{1}{5^{100}}}{4}\)
Vậy \(A=\frac{1-\frac{1}{5^{100}}}{4}\)
\(C=\left(\frac{2}{3}-\frac{1}{4}+\frac{5}{11}\right):\left(\frac{5}{12}+1-\frac{7}{11}\right)\)
\(D=1\frac{1}{3}+\frac{1}{8}:\left(0,75-\frac{1}{2}\right)-\frac{25}{100}.\frac{1}{2}\)
\(E=\left(-\frac{1}{2}\right)^2-\left(-2\right)^2-5^0\)
chứng minh rằng A<\(\frac{1}{16}\) với A =\(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{99}{5^{100}}\)
1.chứng minh rằng A<\(\frac{1}{16}\) biết A=\(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+.....+\frac{99}{5^{100}}\)
2.tính (M-N)\(^3\) biết:
M=1-\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2017}-\frac{1}{2018}+\frac{1}{2019}\)
N=\(\frac{1}{1010}+\frac{1}{1011}+.....+\frac{1}{2019}\)
Chứng minh rằng:
\(S=\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
1.Chứng minh: A < 1/16 với A = \(\frac{1}{5^2}\) + \(\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{99}{5^{100}}\)
mk cần gấp, cảm ơn các bạn
1, Tìm X
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right).100-\left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=89\)
\(\left(20+9\frac{1}{4}\right):2\frac{1}{4}\) \(\left(6-2\frac{4}{5}\right).3\frac{1}{8}-1\frac{3}{5}:\frac{1}{4}\)
\(\frac{32}{15}:\left(-1\frac{1}{5}+1\frac{1}{3}\right)\) \(0,2.\frac{15}{36}-\left(\frac{2}{5}=\frac{2}{3}\right):1\frac{1}{5}\)
\(\frac{-3}{7}.\frac{5}{9}+\frac{4}{9}.\frac{-3}{7}+2\frac{3}{7}\) \(0,7.2\frac{2}{3}.20.0,375.\frac{5}{8}\)
Chứng minh rằng:
1)B=\(\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...+\frac{3^{98}+1}{3^{98}}< 100\)
2)C=\(\frac{5}{5.8.11}+\frac{5}{8.11.14}+...+\frac{5}{302.305.308}\)<\(\frac{1}{48}\)
3)D=\(\frac{11}{9}+\frac{18}{16}+\frac{27}{25}+...+\frac{1766}{1764}\)
\(40\frac{20}{43}< D< 40\frac{20}{21}\)
Bài 1: Tính a) \(\left(\frac{11}{12}:\frac{44}{16}\right)\cdot\left(\frac{-1}{3}+\frac{1}{2}\right)\) b) \(\frac{\left(-5^2\right)\cdot\left(-5\right)^3\cdot16}{5^4\cdot\left(-2\right)^4}\) c) \(7,5:\left(\frac{-5}{3}\right)+2\frac{1}{2}:\left(\frac{-5}{3}\right)\)d) \(\left(\frac{-1}{2}+\frac{1}{3}\right)\cdot\frac{4}{5}+\left(\frac{2}{3}+\frac{1}{2}\right):\frac{4}{5}\)