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a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8
= 1 + 1 + 8
= 2 + 8
= 10
b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)+ \(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8
= \(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8
= \(\dfrac{1}{2}\) + 4
= \(\dfrac{9}{2}\)
Rút gọn tất cả các phân số ta có:
\(\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}+\frac{5}{10}+\frac{6}{10}+\frac{7}{10}+\frac{8}{10}+\frac{9}{10}\)
\(=\frac{1+2+3+4+5+6+7+8+9}{10}=\frac{45}{10}=\frac{9}{2}\)
\(\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+....+\frac{81}{90}\)
\(=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+...+\frac{9}{10}\)
\(=\frac{\left(1+2+3+.....+9\right)}{10}\)
\(=\frac{45}{10}=\frac{9}{2}\)
\(S=\frac{1}{10}+\frac{2^2}{20}+\frac{3^2}{30}+....+\frac{9^2}{90}=\frac{1}{10}+\frac{2}{10}+...+\frac{9}{10}=\frac{45}{10}=\frac{9}{2}\)
\(\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+\frac{16}{40}+\frac{25}{50}\) \(+\frac{36}{60}+\frac{49}{70}+\frac{64}{80}+\frac{81}{90}\)
\(=\frac{1}{10}+\frac{1}{5}+\frac{3}{10}+\frac{2}{5}+\frac{1}{2}+\frac{3}{5}+\frac{7}{10}+\frac{4}{5}+\frac{9}{10}\)
\(=\left(\frac{1}{10}+\frac{9}{10}\right)+\left(\frac{1}{5}+\frac{4}{5}\right)+\left(\frac{3}{10}+\frac{7}{10}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)+\frac{1}{2}\)
\(=1+1+1+1+0,5\)
\(=4+0,5\)
\(=4,5\)
\(\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+.....+\frac{81}{90}\)
\(=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+...+\frac{9}{10}\)
\(=\frac{\left(9+1\right)\times\left(9+1-1\right):2}{10}\)
\(=\frac{10\times9:2}{10}\)
\(=\frac{45}{10}=4,5\)
a.1/2 + 2/4 + 3/6 + 4/8 + 5/10 + 6/12 + 7/14 +8/16 + 9/18 + 10/20
=1/2 + 1/2 + 1/2 +1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2
=1/2 x10
=5
b.1/10 + 4/20 + 9/30 + ... + 64/80 + 81/90
=1/10 + 2/10 + 3/10 +....+ 8/10 + 9/10
= 45/10 =4.5
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