Tinh nhanh : \(\frac{3x5x7x9}{5x7x9x12};\frac{2}{5}:\frac{3}{7}x\frac{3}{7}:\frac{2}{5}\)
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Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)
\(A=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)
chỗ nãy rồi bạn tự tính tiếp
Bài làm
\(-\frac{27}{16}.\frac{4}{9}.\frac{5}{-7}.\frac{14}{5}\)
\(=\left(-\frac{3}{4}.\frac{1}{1}\right).\left(\frac{1}{-1}.\frac{2}{1}\right)\)
\(=-\frac{3}{4}.\frac{2}{-1}\)
\(=\frac{3}{2}\)
# Học tốt #
p=1/(3*5)+1/(5*7)+.....+1/(2015*2017)+1/(2017*2019)
<=> p = 1/3-1/5+1/5-1/7+1/7-......+1/2017-1/2019
<=> p = 1/3 - 1/2019
<=> p = 224/673
\(P=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2015.2017}+\frac{1}{2017.2019}\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2019}\right)\)
\(=\frac{112}{673}\)
\(\left(11\frac{5}{7}+3\frac{8}{11}\right)-9\frac{5}{7}\)
\(=11\frac{5}{7}+3\frac{8}{11}-9\frac{5}{7}\)
\(=\left(11+3-9\right)+\left(\frac{5}{7}+\frac{8}{11}-\frac{5}{7}\right)\)
\(=5+\frac{8}{11}\)
\(=5\frac{8}{11}\)