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\(=\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{59.61}\)
\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{59}-\frac{1}{61}\right)\)
=\(2.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(=2.\left(\frac{36}{505}\right)\)
\(=\frac{72}{505}\)
TK nha !!
Ta có : \(\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+....+\frac{4}{59.61}\)
\(=2\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+.....+\frac{2}{59.61}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{59}-\frac{1}{61}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(=2.\frac{56}{305}=\frac{112}{305}\)
\(\frac{1}{2!}+\frac{2!}{4!}+...+\frac{198!}{200!}=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{199.200}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-...+\frac{1}{199}-\frac{1}{200}=\left(\frac{1}{1}+\frac{1}{2}+...+\frac{1}{200}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200}\right)\)
\(=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)
\(\frac{-5}{3}-\left(\frac{4}{5}-\frac{1}{2}\right)-\left|\frac{3}{4}-\frac{5}{2}+\frac{1}{3}\right|\)
\(=\frac{-5}{3}-\frac{4}{5}+\frac{1}{2}-\left|\frac{3}{4}+\frac{-5}{2}+\frac{1}{3}\right|\)
\(=\frac{-5}{3}-\frac{4}{5}+\frac{1}{2}-\left(\frac{3}{4}+\frac{-5}{2}+\frac{1}{3}\right)\)
\(=\frac{-5}{3}-\frac{4}{5}+\frac{1}{2}-\frac{3}{4}+\frac{5}{2}-\frac{1}{3}\)
\(=\left(\frac{-5}{3}-\frac{1}{3}\right)+\left(\frac{1}{2}+\frac{5}{2}\right)-\left(\frac{4}{5}+\frac{3}{4}\right)\)
\(=\frac{-6}{3}+\frac{6}{2}-\left(\frac{16}{20}+\frac{15}{20}\right)\)
\(=-2+3-\frac{31}{20}\)
\(=1-\frac{31}{20}=\frac{-11}{20}\)
\(\frac{-5}{3}-\left(\frac{4}{5}-\frac{1}{2}\right)-\left|\frac{3}{4}-\frac{5}{2}+\frac{1}{3}\right|\)
\(=\frac{-5}{3}-\frac{4}{5}+\frac{1}{2}-\left|\frac{3}{4}+\frac{-5}{2}+\frac{1}{3}\right|\)
\(=\frac{-5}{3}-\frac{4}{5}+\frac{1}{2}-\left(\frac{3}{4}+\frac{-5}{2}+\frac{1}{3}\right)\)
\(=\frac{-5}{3}-\frac{4}{5}+\frac{1}{2}-\frac{3}{4}+\frac{5}{2}-\frac{1}{3}\)
\(=\left(\frac{-5}{3}-\frac{1}{3}\right)+\left(\frac{1}{2}+\frac{5}{2}\right)-\left(\frac{4}{5}+\frac{3}{4}\right)\)
\(=\frac{-6}{3}+\frac{6}{2}-\left(\frac{16}{20}+\frac{15}{20}\right)\)
\(=\frac{-6}{3}+\frac{6}{2}-\left(\frac{16}{20}+\frac{15}{20}\right)\)
\(=1-\frac{31}{20}=\frac{-11}{20}\)
\(A=8\frac{4}{17}-\left(2\frac{5}{9}+3\frac{4}{17}\right)\)
\(A=8\frac{4}{17}-2\frac{5}{9}-3\frac{4}{17}\)
\(A=\left(8\frac{4}{17}-3\frac{4}{17}\right)-\frac{23}{9}\)
\(A=5-\frac{23}{9}\)
\(A=\frac{45}{9}-\frac{23}{9}\)
\(A=\frac{22}{9}\)
\(A=8\frac{4}{7}-2\frac{5}{9}-3\frac{4}{7}\)
\(A=\left(8\frac{4}{7}-3\frac{4}{7}\right)-2\frac{5}{9}\)
\(A=5-2\frac{5}{9}\)
\(A=4+1-2\frac{5}{9}\)
\(A=4+1-\frac{23}{9}\)
\(A=4+\frac{-14}{9}\)
\(A=1\frac{5}{9}\)
A=\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2018.2020}\)
\(\frac{1}{2}\)A= \(\frac{1}{2}.\left(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2018.2020}\right)\)
\(\frac{1}{2}A\)= \(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2018.2020}\)
\(\frac{1}{2}A\)= \(\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2020-2018}{2018.2020}\)
\(\frac{1}{2}A\)= \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\)
\(\frac{1}{2}A\)= \(\frac{1}{2}-\frac{1}{2020}\)
\(\frac{1}{2}A=\frac{1009}{2020}\)
\(A=\frac{1009}{2020}:\frac{1}{2}\)
\(A=\frac{1009}{1010}\)
a) Ta có
A= 4/2*4+4/4*6+....+4/2018*2020
=> A= 2*(2/2*4+2/4*6+...+2*(2018*2020)
=> A= 2*(1/2-1/4+1/4-1/6+...+1/2018-1/2020)
=> A= 2*(1/2-1/2020)
=> A= 2* 1009/2020
=> A= 1009/1010
b) B= 1/18+1/54+1/108+...+1/990
=> B= 3/3*(1/18+1/54+1/108+..+1/990)
=> B= 1/3*( 3/3*6+3/6*9+...+3/30*33)
=> B= 1/3*(1/3-1/6+1/6-1/9+1/9-1/12+...+1/30-1/33)
=> B= 1/3*( 1/3-1/33)
=> B=1/3*10/33
=> B=10/99
\(\frac{x-2}{2}-\frac{1+x}{3}=\frac{4-3x}{4}-1\)
\(\Leftrightarrow\frac{3\left(x-2\right)-2\left(1+x\right)}{6}=\frac{4-3x-4}{4}\)
\(\Leftrightarrow\frac{3x-6-2-2x}{6}=-\frac{3x}{4}\)
\(\Leftrightarrow\frac{x-8}{6}=-\frac{3x}{4}\)
\(\Leftrightarrow4x-32=-18x\)
\(\Rightarrow x=\frac{16}{11}\)
\(\frac{4}{3.6}+\frac{4}{6.9}+...+\frac{4}{34.37}\)
\(=4\left(\frac{1}{3.6}+\frac{1}{6.9}+...+\frac{1}{34.37}\right)\)
\(=4.3\left(\frac{1}{3.6}+\frac{1}{6.9}+...+\frac{1}{34.37}\right):3\)
\(=4\left(\frac{3}{3.6}+\frac{3}{6.9} +...+\frac{3}{34.37}\right):3\)
\(=4.\frac{34}{111}:3\)
\(=\frac{136}{333}\)
\(\frac{4}{3.6}+\frac{4}{6.9}+...+\frac{4}{31.34}+\frac{4}{34.37}\)
\(=4\left(\frac{1}{3.6}+\frac{1}{6.9}+...+\frac{1}{31.34}+\frac{1}{34.37}\right)\)
\(=4\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{31}-\frac{1}{34}+\frac{1}{34}-\frac{1}{37}\right)\)
\(=4\left(\frac{1}{3}-\frac{1}{37}\right)\)
\(=4.\frac{34}{111}\)
\(=\frac{136}{111}\)