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13 tháng 3 2020
a,\(0,5-\frac{5}{41}+\frac{1}{2}-\frac{36}{41}\)
=\(\frac{1}{2}-\frac{5}{41}+\frac{1}{2}-\frac{36}{41}\)
=\(\left(\frac{1}{2}+\frac{1}{2}\right)-\left(\frac{5}{41}+\frac{36}{41}\right)\)
= \(1-1=0\)
b,\(\left(\frac{-1}{3}\right)^2.\frac{4}{11}+\frac{7}{11}.\left(\frac{1}{3}\right)^2\)
=\(\frac{1}{9}.\frac{4}{11}+\frac{7}{11}.\frac{1}{9}\)
=\(\frac{1}{9}\left(\frac{4}{11}+\frac{7}{11}\right)\)
=\(\frac{1}{9}.1=\frac{1}{9}\)
c,\(\left(\frac{-2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
=\(\left(\frac{-2}{3}+\frac{3}{7}-\frac{1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
=\(\left(-1+1\right).\frac{5}{4}=0.\frac{5}{4}\)=0
14 tháng 2 2020
\(C=...\)
\(=\frac{1}{3^2}+\frac{1}{4^2}-\frac{1}{4^2}+\frac{1}{5^2}-\frac{1}{5^2}+...-\frac{1}{14^2}+\frac{1}{14^2}-\frac{1}{15^2}\)
\(=\frac{1}{3^2}-\frac{1}{15^2}\)
\(=\frac{1}{9}-\frac{1}{225}\)
Do \(\frac{1}{9}-\frac{1}{225}\)<\(\frac{1}{5}\)
\(=>C< \frac{1}{5}\)( ĐPCM )
14 tháng 2 2020
C = ...
=> C = \(\frac{1}{3^2}-\frac{1}{4^2}+\frac{1}{4^2}-\frac{1}{5^2}+...+\frac{1}{14^2}-\frac{1}{15^2}\)
C = \(\frac{1}{3^2}-\frac{1}{15^2}\)
Ta thấy : \(\frac{1}{3^2}< \frac{1}{5}\Leftrightarrow\frac{1}{3^2}-\frac{1}{15^2}< \frac{1}{5}\)
=> C < \(\frac{1}{5}\)
12 tháng 11 2017
a, (-0.25) * 7.9 * 40 = [ (-0.25) * 40] * 7.9 = -10 * 7.9 = -79
b, ( 3/2 )^3 * 2^3 = ( 3/2*2) ^3 = 3^3 = 27
c, (1.75 / \(\frac{7}{2}\)) * \(\frac{4}{5}\)= ( 7/4 * 7/2 ) *4/5 = \(\frac{49}{10}\)
d, \(\frac{11}{2}\cdot4\frac{5}{3}-2\frac{5}{3}\cdot\frac{11}{2}\)= \(\frac{11}{2}\cdot\left(\frac{17}{3}-\frac{11}{3}\right)\)= \(\frac{11}{2}\cdot\frac{6}{3}\)= \(\frac{11}{2}\cdot2\)=11
ML
3 tháng 8 2017
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)
\(B=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\)
\(B=\frac{1}{3}-\frac{1}{111}\)
\(B=\frac{12}{37}\)
\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(C=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(C=7\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(C=7.\frac{3}{35}\)
\(C=\frac{3}{5}\)
TP
3 tháng 8 2017
Ta có:
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(A=\frac{1}{1}-\frac{1}{100}=\frac{99}{100}\)
\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)
\(B=4.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\right)\)
\(B=4.\left(\frac{1}{3}-\frac{1}{111}\right)=4.\frac{12}{37}=\frac{48}{37}\)
\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(C=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)
\(C=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)
5 tháng 8 2019
1. Tính hợp lí :
a) \(\frac{6}{7}.\frac{5}{11}+\frac{5}{7}.\frac{2}{11}-\frac{5}{7}.\frac{14}{11}\)
\(=\frac{5}{7}.\left(\frac{6}{11}+\frac{2}{11}-\frac{14}{11}\right)\)
\(=\frac{5}{7}.\frac{-6}{11}=-\frac{30}{77}\)
b) \(\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}-\frac{1}{3}\)
\(\frac{1}{3}.\left(\frac{4}{5}+\frac{6}{5}-\frac{1}{3}\right)\)
\(=\frac{1}{3}.\frac{5}{3}=\frac{5}{9}\)
DB
0
23 tháng 10 2017
\(A=\dfrac{3}{1^2.2^2}+\dfrac{7}{3^2.4^2}+\dfrac{11}{5^2.6^2}+\dfrac{15}{7^2.8^2}+\dfrac{19}{9^2.10^2}\)
\(A=\dfrac{1+2}{1^2.2^2}+\dfrac{3+4}{3^2.4^2}+\dfrac{5+6}{5^2.6^2}+\dfrac{7+8}{7^2.8^2}+\dfrac{9+10}{9^2.10^2}\)
\(A=\dfrac{1}{1.2^2}+\dfrac{1}{1^2.2}+\dfrac{1}{3.4^2}+\dfrac{1}{3^2.4}+\dfrac{1}{5.6^2}+\dfrac{1}{5^2.6}+...+\dfrac{1}{9^2.10}\)
\(A=\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{48}+\dfrac{1}{36}+\dfrac{1}{180}+\dfrac{1}{150}+....+\dfrac{1}{900}\)
\(\left\{{}\begin{matrix}\dfrac{1}{48}< \dfrac{3}{32}\\\dfrac{1}{36}< \dfrac{1}{32}\\........\\\dfrac{1}{900}< \dfrac{1}{32}\end{matrix}\right.\)
Nên \(A< \dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{32}.8=1\)
\(\frac{-1}{4}\)\(^2\).\(\frac{4}{11}\)+\(\frac{7}{11}\).\(\frac{-1}{4}\)\(^2\)
=(\(\frac{-1}{4}\))\(^2\)(\(\frac{4}{11}\)+\(\frac{7}{11}\))
=\(\frac{1}{16}\).\(\frac{11}{11}\)
=\(\frac{1}{16}\).1
=\(\frac{1}{16}\)