Tính
\(A=\frac{2.2016}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+...2016}}\)
Tinh hop li:
\(F=\frac{2.2016}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2016}}\)
tính :
a) \(\frac{4}{9}:\frac{-1}{7}+6\frac{5}{9}:\frac{-1}{7}\)
b) \(\left(2\frac{1}{3}+3\frac{1}{2}\right):\left(-4\frac{1}{6}+3\frac{1}{7}\right)+7\frac{1}{2}\)
c) \(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{7}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
CMR : E = \(1-\frac{1}{2^2}-\frac{1}{3^2}-...-\frac{1}{2004^2}>\frac{1}{2004}\)
F = \(\frac{1}{2^2}+\frac{1}{4^2}+...+\frac{1}{200^2}< \frac{1}{2}\)
H = \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
2 Thực hiện phép tính
\(\frac{17}{9}-\frac{17}{9}:\left(\frac{7}{3}+\frac{1}{2}\right)\)
\(\frac{4}{3}.\frac{2}{5}-\frac{3}{4}.\frac{2}{5}\)
\(-\frac{3}{4}.5\frac{3}{13}-0.75.\frac{36}{13}\)
\(3.\left(-\frac{4}{3}\right)^2-\frac{7}{3}\)
\(-\frac{5}{7}.\frac{3}{11}+\frac{-5}{7}.\frac{8}{11}+3\frac{5}{7}\)
\(32\frac{1}{7}:\left(\frac{-5}{4}\right)-47\frac{1}{7}:\left(\frac{-5}{4}\right)\)
\(\left(\frac{2}{3}+\frac{1}{2}\right)^2-\frac{1}{12}\\ \frac{1}{4}-\frac{5}{12}:\frac{1}{6}+\frac{-6}{5}\\ \frac{17}{21}+\frac{5}{23}-\frac{1}{2}+\frac{4}{21}-1\frac{5}{23}\)
\(\left(-3\right)^2+\sqrt{\frac{16}{25}}-\sqrt{9}+\frac{\sqrt{81}}{3}\)
Tính:
a) \(\left(\frac{3}{7}+\frac{1}{2}\right)^2\)
b) \(\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
c) \(\frac{5^4.20^4}{25^5.4^5}\)
d) \(\left(\frac{-10}{3}\right)^5.\left(\frac{-6}{5}\right)^4\)
e) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2\)
f) \(2:\left(\frac{1}{2}-\frac{2}{3}\right)^3\)
Tính :
A = \(\left(1-\frac{2}{3}+\frac{4}{3}\right)-\left(\frac{4}{5}-1\right)+\left(\frac{7}{5}+2\right)\)
B = \(\left(-3+\frac{3}{4}-\frac{1}{3}\right):\left(5+\frac{2}{5}-\frac{2}{3}\right)\)
C = \(\left(\frac{3}{5}-\frac{4}{5}\right).\left(\frac{2}{7}-\frac{3}{14}\right)-\left(\frac{5}{9}-\frac{7}{27}\right).\left(1-\frac{3}{5}\right)+\left(1-\frac{11}{12}\right).\left(1-\frac{11}{12}\right)\)
Tính :
\(D=\frac{\left(\frac{3}{10}-\frac{4}{5}-\frac{7}{20}\right).\frac{-5}{19}}{\left(\frac{1}{14}+\frac{1}{7}-\frac{-3}{35}\right).\frac{4}{3}}\)
\(E=\frac{1-\frac{1}{3}+\frac{1}{1+\frac{1}{3}}}{1-\frac{1}{3}-\frac{1}{1\frac{1}{3}}}\)
\(G=1-\frac{1}{1-\frac{2}{1-\frac{3}{1-\frac{1}{4}}}}\)
1) Tính:
a) \(\frac{\left(1+\frac{17}{1}\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right).....\left(1+\frac{17}{19}\right)}{\left(1+\frac{19}{1}\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right).....\left(1+\frac{19}{17}\right)}\)
b) \(\frac{\frac{-6}{5}+\frac{6}{19}-\frac{6}{23}}{\frac{9}{5}-\frac{9}{19}+\frac{9}{23}}\)
c) \(\frac{\frac{1}{6}-\frac{1}{39}+\frac{1}{51}}{\frac{1}{8}-\frac{1}{52}+\frac{1}{68}}\)
d) \(\frac{\frac{2}{3}-\frac{2}{5}-\frac{2}{7}+\frac{2}{11}}{\frac{13}{3}-\frac{13}{5}-\frac{13}{7}+\frac{13}{11}}\)
e) \(\frac{\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2017}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}}\)
2) CMR: \(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{800}}< \frac{1}{3}\)
