Thực hiện phép tính:
\(\frac{5}{12}\)+(\(\frac{-31}{41}\))
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Đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{99\cdot101}\)
\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{99}-\frac{1}{101}\)
\(2A=\frac{100}{101}\)
\(A=\frac{50}{101}\)
b) \(\frac{2^{10}+3^{31}+2^{40}+3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}=\frac{2^{10}+2^{40}}{2^{11}+2^{41}}\)
\(\frac{2^{10}+2^{40}}{2^{11}+2^{41}}=\frac{1}{2}\)
=1/2x(1/1.3+1/3.5+...+1/99.101)
=1/2.(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=1/2.(1-1/101)
=1/2.100/101
=50/101
chúc bạn học tốt
\(\frac{2^{10}.3^{31}+2^{90}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\) \(\frac{2^{10}.3^6.\left(3^{25}+2^{30}\right)}{2^{10}.3^6\left(3^{25}+2^{30}\right)}\) \(=1\)
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Thông cảm cho mình
~~~ Chúc bạn học giỏi ~~~
\(\begin{array}{l}\frac{{ - 4}}{3} - \frac{{12}}{5} = \frac{{ - 4}}{3} + \frac{{ - 12}}{5}\\ = \frac{{ - 20}}{{15}} + \frac{{ - 36}}{{15}} = \frac{{ - 56}}{{15}}\end{array}\).
\(a.=\frac{3}{15}+\frac{-10}{15}\)
\(=-\frac{7}{15}\)
\(b.=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)
\(=1+\left(-1\right)\)
\(=0\)
\(c.=\left(\frac{13}{25}-\frac{38}{25}\right)+\left(\frac{6}{41}+\frac{35}{41}\right)-\frac{1}{2}\)
\(=-1+1-\frac{1}{2}\)
\(=0-\frac{1}{2}\)
\(=-\frac{1}{2}\)
\(d.=\frac{5}{6}.\left(18\frac{2}{3}-6\frac{2}{3}\right)\)
\(=\frac{5}{6}.12\)
\(=10\)
B=47/41.[12.(1+1/19-1/37-1/53)/3.(1+1/19-1/37-1/53):4.(1+1/17+1/19+1/2006)/5.(1+1/17+1/19+1/2006)].123/235
=47/41.[4:4/5].123/235
=47/41.5.123/235=3
C=63.10101.37-37.10101.63/1+2+3+...+2006
=0/1+2+3+...+2006=0
CẬU XEM LẠI CHO MÌNH NHA!
\(\left(\frac{-31}{37}\right)^5.\left(\frac{37}{62}\right)^5\)
\(=\left(\frac{-31}{37}.\frac{37}{62}\right)^5\)
\(=\left(\frac{-1}{2}\right)^5\)
\(=\frac{-1}{32}\)
\(\left(\frac{-31}{37}\right)^5.\left(\frac{37}{62}\right)^5\)
\(=\left(\frac{-31}{37}.\frac{37}{62}\right)^5\)
\(=\left(\frac{-1}{2}\right)^5\)
\(=\frac{-1}{32}\)
học tốt