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\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\\ =\left(\frac{2}{1}-\frac{2}{2}\right)+\left(\frac{2}{2}-\frac{2}{3}\right)+...+\left(\frac{2}{5}-\frac{2}{6}\right)\\ =\frac{2}{1}+\left(\frac{2}{2}-\frac{2}{2}\right)+....+\left(\frac{2}{5}-\frac{2}{5}\right)-\frac{2}{6}\\ \)
\(=\frac{2}{1}-\frac{2}{6}\\ =\frac{10}{6}=\frac{5}{3}\)
Câu b và c tương tự như câu a
d) Số hạng thứ 225 của dãy là :
5+(225-1).5=1125
Tổng của dãy trên là :
(1125+5).225:2=127125
e) Số số hạng là :
(2016-2):2+1=1008 ( số hạng )
Tổng của dãy trên là :
(2016+2).1008:2=1017072
a)\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\)
\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(=2.\left(1-\frac{1}{6}\right)\)
\(=2.\frac{5}{6}\)
\(=\frac{5}{3}\)
b)\(\frac{2}{1.3}+\frac{2}{5.3}+\frac{2}{5.7}+\frac{2}{9.7}+...+\frac{2}{2015.2017}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2015}-\frac{1}{2017}\)
\(=1-\frac{1}{2017}\)
\(=\frac{2016}{2017}\)
c)\(\frac{12}{2.5}+\frac{12}{8.5}+\frac{12}{11.8}+\frac{12}{14.11}+\frac{12}{17.14}+\frac{12}{20.17}\)
\(=4.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)
\(=4.\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=4.\frac{9}{20}\)
\(=\frac{9}{5}\)
Tính
\(\frac{15}{25}+\frac{80}{125}+\frac{12}{42}+\frac{78}{100}+\frac{18}{12}\)
\(\frac{3}{5}+\frac{16}{25}+\frac{6}{21}+\frac{39}{50}+\frac{3}{2}\)
\(\frac{15}{25}+\frac{16}{25}+\frac{39}{50}+\frac{6}{21}+\frac{3}{2}\)
\(\frac{62}{50}+\frac{39}{50}+\frac{12}{42}+\frac{63}{42}\)
\(\frac{101}{50}+\frac{75}{42}\)
\(\frac{4242}{2100}+\frac{3750}{2100}\)
\(\frac{7992}{2100}\)
7/19 . 8/11 + 3/19 . 7/11 + ( -12/19 )
= 7/19 + 3/19 . 8/11 + 7/11 + ( -12/19 )
= 10/19 . 15/11 + ( -12/19 )
= 15/11 . 10/19 + ( -12/19 )
= 15/11 . ( -2/19 )
= -30/209
g) \(\frac{x+2}{98}+\frac{x+4}{96}=\frac{x+6}{94}+\frac{x+8}{92}\)
\(\Leftrightarrow\left(\frac{x+2}{98}+1\right)+\left(\frac{x+4}{96}+1\right)=\left(\frac{x+6}{94}+1\right)+\left(\frac{x+8}{92}+1\right)\)
\(\Leftrightarrow\left(\frac{x+2+98}{98}\right)+\left(\frac{x+4+96}{96}\right)=\left(\frac{x+6+94}{94}\right)+\left(\frac{x+8+92}{92}\right)\)
\(\Leftrightarrow\frac{x+100}{98}+\frac{x+100}{96}=\frac{x+100}{94}+\frac{x+100}{92}\)
\(\Leftrightarrow\frac{x+100}{98}+\frac{x+100}{96}-\frac{x+100}{94}-\frac{x+100}{92}=0\)
\(\Leftrightarrow\left(x+100\right).\left(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\right)=0\)
Vì \(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\ne0.\)
\(\Leftrightarrow x+100=0\)
\(\Leftrightarrow x=0-100\)
\(\Leftrightarrow x=-100.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{-100\right\}.\)
h) \(\frac{x-12}{77}+\frac{x-11}{78}=\frac{x-74}{15}+\frac{x-73}{16}\)
\(\Leftrightarrow\left(\frac{x-12}{77}-1\right)+\left(\frac{x-11}{78}-1\right)=\left(\frac{x-74}{15}-1\right)+\left(\frac{x-73}{16}-1\right)\)
\(\Leftrightarrow\left(\frac{x-12-77}{77}\right)+\left(\frac{x-11-78}{78}\right)=\left(\frac{x-74-15}{15}\right)+\left(\frac{x-73-16}{16}\right)\)
\(\Leftrightarrow\frac{x-89}{77}+\frac{x-89}{78}=\frac{x-89}{15}+\frac{x-89}{16}\)
\(\Leftrightarrow\frac{x-89}{77}+\frac{x-89}{78}-\frac{x-89}{15}-\frac{x-89}{16}=0\)
\(\Leftrightarrow\left(x-89\right).\left(\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16}\right)=0\)
Vì \(\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16}\ne0.\)
\(\Leftrightarrow x-89=0\)
\(\Leftrightarrow x=0+89\)
\(\Leftrightarrow x=89.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{89\right\}.\)
Chúc bạn học tốt!
b, 125 - 25:3 x 12 = 125 - \(\frac{25}{3}\)x 12 = 125 - 100 = 25
a, 50% + \(\frac{7}{12}\)- \(\frac{1}{2}\) = \(\frac{50}{100}+\frac{7}{12}-\frac{1}{2}=\frac{1}{2}-\frac{1}{2}+\frac{7}{12}=0+\frac{7}{12}=\frac{7}{12}\)
= \(\frac{11}{10}\cdot\frac{12}{11}\cdot\frac{13}{12}\cdot\frac{14}{13}\cdot\frac{15}{14}\cdot\frac{16}{15}\cdot\frac{17}{16}\)
=11/10 x 12/11 x 13/12 x 14/13 x 15/14 x 16/15 x 17/16
= \(\frac{17}{10}\)
=\(\frac{11}{10}\)x \(\frac{12}{11}\)x .......... x \(\frac{16}{15}\)x\(\frac{17}{16}\)
= \(\frac{11^1x12^1x......x16^1x17}{10x11^1x...x15^1x16^1}\)( những số có số nhỏ ở trên là rút gọn với số khác VD:11 rút gọn cho 11 )
=\(\frac{1x1x......x1x17}{10x1x.......x1x1}\)
=\(\frac{17}{10}\)
= 1,7
\(=\frac{3.5.\left(2^2\right)^{12}.\left(3^2\right)^7-2^2.3^{15}.\left(2^3\right)^8}{19.2^{24}.3^{14}-2.3.\left(2^2\right)^{12}.\left(3^3\right)^5}\)
\(=\frac{3.5.2^{24}.3^{14}-2^2.3^{15}.2^{24}}{19.2^{24}.3^{14}-2.3.2^{24}.3^{15}}\)
\(=\frac{5.2^{24}.3^{15}-3^{15}.2^{26}}{19.2^{24}.3^{14}-2^{25}.3^{16}}\)
\(=\frac{2^{24}.3^{15}.\left(5-2^2\right)}{2^{24}.3^{14}.\left(19-3^2\right)}\)
\(=\frac{3.1}{10}\)
\(=\frac{3}{10}\)
\(\frac{125}{34}+\frac{78}{12}=10\frac{3}{17}=\frac{173}{17}\)
\(\frac{12}{78}\times\frac{23}{12}=\frac{23}{78}\)
\(\frac{98}{24}-\frac{12}{97}=3\frac{1117}{1164}=\frac{4609}{1164}\)
\(\frac{12}{33}:\frac{5}{12}=\frac{48}{55}\)
-----------HOK TỐT----------
125/34 + 78/12 = 173/17
12/78 x 23/12 = 23/78