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Ta có: \(\dfrac{1}{5}+\dfrac{4}{10}+\dfrac{9}{15}+\dfrac{16}{20}+\dfrac{25}{25}+\dfrac{36}{30}+\dfrac{49}{35}+\dfrac{64}{40}+\dfrac{81}{45}\)
\(=\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}+\dfrac{5}{5}+\dfrac{6}{5}+\dfrac{7}{5}+\dfrac{8}{5}+\dfrac{9}{5}\)
\(=\dfrac{45}{5}=9\)
1/5+4/10+9/15+16/20+25/25+36/30+49/35+64/40+81/45 = 1/5 + 2/5 + 3/5 + 4/5 + 1 + 6/5 + 7/5 + 8/5 + 9/5 = (1/5 + 9/5) + (2/5 + 8/5) + (3/5 + 7/5) + (4/5 + 6/5) + 1 = 2 + 2 + 2 + 2 + 1 = 9
\(\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+....+\frac{81}{90}\)
\(=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+...+\frac{9}{10}\)
\(=\frac{\left(1+2+3+.....+9\right)}{10}\)
\(=\frac{45}{10}=\frac{9}{2}\)
\(S=\frac{1}{10}+\frac{2^2}{20}+\frac{3^2}{30}+....+\frac{9^2}{90}=\frac{1}{10}+\frac{2}{10}+...+\frac{9}{10}=\frac{45}{10}=\frac{9}{2}\)
Rút gọn tất cả các phân số ta có:
\(\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}+\frac{5}{10}+\frac{6}{10}+\frac{7}{10}+\frac{8}{10}+\frac{9}{10}\)
\(=\frac{1+2+3+4+5+6+7+8+9}{10}=\frac{45}{10}=\frac{9}{2}\)