\(\frac{5}{4\cdot6}+\frac{5}{6\cdot8}+...+\frac{5}{298\cdot300}\)
\(=\frac{5}{2}\cdot\left(\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{298\cdot300}\right)\)
\(=\frac{5}{2}\cdot\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{298}-\frac{1}{300}\right)\)
\(=\frac{5}{2}\cdot\left(\frac{1}{4}-\frac{1}{300}\right)\)
\(=\frac{37}{60}\)
Tính nhanh
\(5\frac{2}{7}.\frac{8}{11}\)+ \(5\frac{2}{7}.\frac{5}{11}\)-\(5\frac{2}{7}.\frac{2}{11}\)
Tính nhanh (nếu có thể):
\(a,\frac{\frac{3}{41}-\frac{12}{47}+\frac{27}{53}}{\frac{4}{41}-\frac{16}{47}+\frac{36}{53}}+\frac{-0,25.\frac{-2}{3}-75\%:(\frac{-1}{2}+\frac{2}{3})}{|-1\frac{1}{2}|.(\frac{-2}{3}-0,75:\frac{3}{-2})}\)
\(b,A=158.(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}).\frac{50550505}{711711711}\)
Tính giá trị của biểu thức:
\(A=\frac{5}{2}+\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+\frac{5}{42}+\frac{5}{56}+\frac{5}{72}\)
Tính nhanh ( nếu có thể):
\(a,-3^2+\left\{-52:[\left(-3\right)^2\right\}\) \(d,(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}):(\frac{1}{6}-\frac{1}{8}-\frac{1}{24})\)
\(b,2\frac{3}{7}+(\frac{2}{9}-1\frac{3}{7})-\frac{5}{3}:\frac{1}{9}\) \(e,\frac{-5}{13}:\frac{3}{7}-\frac{2}{7}.\frac{8}{13}+\frac{5}{13}.\frac{1}{7}\)
\(c,\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
bài 1
a, \(\left(-\frac{2}{5}\right):\left[\frac{-3}{5}+\frac{3}{2}\right]\)
b,\(\frac{-5}{2016}.\frac{2}{11}+\frac{-5}{2016}.\frac{9}{11}+1\frac{5}{2016}\)
Tính nhanh \(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}...1\frac{1}{999}\)
\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}\)
\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(\frac{3}{41}-\frac{12}{47}+\frac{27}{53}\)
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\(\frac{4}{41}-\frac{16}{47}+\frac{36}{53}\)
Bài 1:Tìm x,biết
a) \(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
b)\(x+\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}=\frac{2}{3}\)
c)\(x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}=\frac{5}{24}\)
d)\(8-\frac{8-\frac{8}{5}+\frac{8}{25}-\frac{8}{125}}{9-\frac{9}{5}+\frac{9}{25}-\frac{9}{125}}:\frac{161616}{151515}=\frac{4+\frac{4}{73}-\frac{4}{115}}{5+\frac{5}{73}-\frac{1}{23}}\)
tính tổng: \(B=\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+\frac{5}{24\cdot27}+...+\frac{5}{123\cdot126}\)
