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a/\(1248:12-2,5\times4+6,03.\)
\(=104-10+6,03\)
\(=94+6,03=100,03\)
b/\(\left(\frac{2}{3}+\frac{5}{7}-\frac{1}{3}\right)\times\frac{7}{11}+3\frac{1}{3}.\)
\(=\left(\frac{29}{21}-\frac{1}{3}\right)\times\frac{7}{11}+3\frac{1}{3}\)
\(=\frac{22}{11}\times\frac{7}{11}+3\frac{1}{3}\)
\(=\frac{2}{3}+3\frac{1}{3}\)
\(=\frac{2}{3}+\frac{10}{3}\)
\(=\frac{12}{3}=4\)
a) \(M=\frac{2\times2}{1\times5}+\frac{2\times2}{5\times9}+\frac{2\times2}{9\times13}+...+\frac{2\times2}{45\times40}\)
\(M=\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+...+\frac{4}{45\times49}\)
\(M=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{45}-\frac{1}{49}\)
\(M=1-\frac{1}{49}\)
\(M=\frac{48}{49}\)
b) \(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+5+...+10}\)
= \(\frac{2}{2\times\left(1+2\right)}+\frac{2}{2\times\left(1+2+3\right)}+...+\frac{2}{2\times\left(1+2+3+...+10\right)}\)
\(=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{110}\)
\(=\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{10\times11}\)
\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(=2\times\frac{9}{22}\)
\(=\frac{9}{11}\)
Mình trả lời câu a nha M= 4/1*5+4/5*9+4/9*13+...+4/45*49 M=1-1/5+1/5-1/9+1/9-1/13+...+1/45-1/49 M=1-1/49=48/49
a)
\(=\dfrac{13}{5}+\dfrac{7}{5}\cdot\dfrac{7}{2}\)
\(=\dfrac{13}{5}+\dfrac{49}{10}\\ =\dfrac{26}{10}+\dfrac{49}{10}\\ =\dfrac{15}{2}\)
b)
\(=\dfrac{52}{4}-\dfrac{11}{3}:\dfrac{7}{6}\)
\(=\dfrac{52}{4}-\dfrac{22}{7}\\ =\dfrac{69}{7}\)
a) $2\dfrac35 + 1\dfrac25 . 3\dfrac12$
$= \dfrac{13}5 + \dfrac75.\dfrac72$
$= \dfrac{26}{10} + \dfrac{49}{10}$
$=\dfrac{15}2$.
b) $4\dfrac34 - 3\dfrac23 : 1\dfrac16$
$= \dfrac{19}4 - \dfrac{11}3 : \dfrac76$
$= \dfrac{19}4 - \dfrac{11}3 . \dfrac67$
$= \dfrac{19}4 - \dfrac{22}7$
$= \dfrac{45}{28}$.
\(\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)\times\left(1-\dfrac{1}{6}\right)\times\dots\times\left(1-\dfrac{1}{99}\right)\times\left(1-\dfrac{1}{100}\right)\) (sửa đề)
\(=\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dots\times\dfrac{98}{99}\times\dfrac{99}{100}\)
\(=\dfrac{2\times3\times4\times5\times\dots\times98\times99}{3\times4\times5\times6\times\dots\times99\times100}\)
\(=\dfrac{2}{100}\)
\(=\dfrac{1}{50}\)
\(A=\frac{1\times111+2\times110+3\times109+...+111\times1}{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+111\right)}\)
\(A=\frac{1\times111+2\times110+3\times109+...+111\times1}{\left(1+1+...+1\right)+\left(2+2+...+2\right)+...+111}\)(\(111\)số hạng \(1\), \(110\)số hạng \(2\),...)
\(A=\frac{1\times111+2\times110+3\times109+...+111\times1}{1\times111+2\times110+3\times109+...+111\times1}\)
\(A=1\)