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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
= \(\dfrac{9}{2}\)
\(2+4+6+8+10+12+14+16+18+20+22\)
\(=\left(2+22\right)+\left(4+20\right)+\left(6+18\right)+\left(8+16\right)+\left(10+14\right)+12\)
\(=24+24+24+24+24+12\)
\(=24\times5+12\)
\(=12\times2\times5+12\)
\(=12\times\left(2\times5+1\right)\)
\(=12\times11=121\)
a: Đặt A=2+4+...+82+84
Số số hạng là (84-2):2+1=42(số)
Tổng là (84+2)*42/2=1806
Đặt B=4+7+...+130+133
Số số hạng là (133-4):3+1=44(số)
Tổng là (133+4)*44/2=3014
=>C=1806/3014=903/1507
b: \(=\dfrac{18\left(123+4567+5310\right)}{132+48}=\dfrac{18\cdot10000}{180}=1000\)
2+4-6-8+10+..................-2008
=2+(4-6-8+10)+(12-14-16+18)+.............+(1996-1998-2000+2002)+(2004-2006-2008)
=2+0+0+...............+0+(-2010)
=2+(-2010)
=-2008