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\(\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...+\frac{1}{24×25}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)
\(=\frac{1}{5}-\frac{1}{25}\)
\(=\frac{5}{25}-\frac{1}{25}\)
\(=\frac{4}{25}\)
\(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{24\times25}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)
\(=\frac{1}{5}-\frac{1}{25}\)
\(=\frac{4}{25}\)\(\left(=0,16\right)\)
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Ta có: \(C=\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}\)
\(\Leftrightarrow C=2\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\right)\)
\(\Leftrightarrow C=2\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)
\(\Leftrightarrow C=2\left(1-\dfrac{1}{7}\right)=\dfrac{2.6}{7}=\dfrac{12}{7}\)
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A = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ........... + 1/99 - 1/100
A = 1/4 - 1/100
A = 6/25
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Ta có 1/4 x 4/1 + 1/5 x 6/1 + 1/6 x 7/1 + 1/7 x 8/1
Ta có 1/4 x 4/1 = 1. => 1 + 6/5 + 7/6 + 8/7
1 + 6/5 + 7/6 + 8/7 = 11/5 + 7/6 + 8/7 = 101/30 + 8/7 = 947/210
P/S: MIK KO BIẾT CÁCH LÀM NHANH NÊN CHỈ THẾ NÀY THÔI !
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\(\frac{2}{5\times6}+\frac{2}{6\times7}+...+\frac{2}{68\times69}\)
\(=\left(\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{68\times69}\right)\times2\times\frac{1}{2}\)
\(=\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{68}-\frac{1}{69}\right)\times1\)
\(=\left(\frac{1}{5}-\frac{1}{69}\right)\times1\)
\(=\frac{64}{345}\times1=\frac{64}{345}\)
#Nii
A = \(\dfrac{3}{5\times6}\) + \(\dfrac{3}{6\times7}\)+...+ \(\dfrac{3}{87\times88}\)
A = 3\(\times\)( \(\dfrac{1}{5\times6}\) + \(\dfrac{1}{6\times7}\)+...+ \(\dfrac{1}{87\times88}\))
A = 3 \(\times\)( \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\) +...+ \(\dfrac{1}{87}\) - \(\dfrac{1}{88}\))
A = 3 \(\times\)( \(\dfrac{1}{5}\) - \(\dfrac{1}{88}\))
A = 3 \(\times\) \(\dfrac{83}{440}\)
A = \(\dfrac{249}{440}\)