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

= \(\dfrac{9}{2}\) 

c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)

= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

=  \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)

= \(\dfrac{10+10+10+10+5}{10}\)

= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)

= \(\dfrac{10\times4+5}{10}\)

= \(\dfrac{45}{10}\)

= \(\dfrac{9}{2}\)

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

  = (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + 8

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

= 1 + 1 + 8

= 2 + 8

= 10

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{9}{18}\) + \(\dfrac{10}{20}\)

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\)

= \(\dfrac{1}{2}\) x 10

= 5

c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)

= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

=  \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)

= \(\dfrac{10+10+10+10+5}{10}\)

= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)

= \(\dfrac{10\times4+5}{10}\)

= \(\dfrac{45}{10}\)

= \(\dfrac{9}{2}\)

1/10 + 4/20 + 9/30 + 16/40 + 25/50 + 36/60 + 49/70 + 64/80 + 81/90 
= 1/10 + 2/10 + 3/10 + 4/10 + 5/10 + 6/10 + 7/10 + 8/10 + 9/10 
=(1+2+3+....+9) /10 
=(1+9)x9:2 /10 
=45/10=4,5 

chắc chắn đúng đó  

\(\frac{1}{5}+\frac{4}{10}+\frac{9}{15}+\frac{16}{20}+1+\frac{36}{30}+\frac{49}{35}+\frac{64}{40}+\frac{81}{45}\)

\(=\left(\frac{1}{5}+\frac{81}{45}\right)+\left(\frac{4}{10}+\frac{49}{35}\right)+\left(\frac{9}{15}+\frac{49}{35}\right)+\left(\frac{16}{20}+\frac{36}{30}\right)+1\)

\(=2+2+2+2+1\)

\(=2\times4+1\)

\(=9\)

~ Hok tốt ~

\(M=\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+\frac{16}{40}+...+\frac{81}{90}\)

\(M=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}+...+\frac{9}{10}\)

\(M=\frac{\left(9+1\right)\cdot\left(9-1+1\right):2}{10}\)

\(M=\frac{10\cdot9:2}{10}=4,5\)

tớ làm giống bạn kia

tớ cũng làm như vậy

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)

\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)

\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=9-\left(1-\frac{1}{10}\right)\)

\(=9-\frac{9}{10}=\frac{81}{10}\)

\(\dfrac{1}{10}+\dfrac{4}{20}+\dfrac{9}{30}+\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)
\(=\dfrac{1}{10}+\dfrac{1}{5}+\dfrac{3}{10}+\dfrac{2}{5}+\dfrac{1}{2}+\dfrac{3}{5}+\dfrac{7}{10}+\dfrac{4}{5}+\dfrac{9}{10}\)
\(=\left(\dfrac{1}{10}+\dfrac{3}{10}+\dfrac{7}{10}+\dfrac{9}{10}\right)+\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}\right)+\dfrac{1}{2}\)
\(=2+2+\dfrac{1}{2}\)
\(=4+\dfrac{1}{2}\)
\(=\dfrac{8}{2}+\dfrac{1}{2}=\dfrac{9}{2}\)

\(\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+....+\frac{81}{90}\)

\(=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+...+\frac{9}{10}\)

\(=\frac{\left(1+2+3+.....+9\right)}{10}\)

\(=\frac{45}{10}=\frac{9}{2}\)

\(S=\frac{1}{10}+\frac{2^2}{20}+\frac{3^2}{30}+....+\frac{9^2}{90}=\frac{1}{10}+\frac{2}{10}+...+\frac{9}{10}=\frac{45}{10}=\frac{9}{2}\)

          Ta có : 

           Đặt \(A=\frac{1}{10}+\frac{4}{20}+\frac{9}{30}+\frac{16}{40}+\frac{25}{50}+\frac{36}{60}+\frac{49}{70}+\frac{64}{80}+\frac{91}{90}\)

                \(A=\frac{1}{10}+\frac{2^2}{20}+\frac{3^2}{30}+\frac{4^2}{40}+\frac{5^2}{50}+\frac{6^2}{60}+\frac{7^2}{70}+\frac{8^2}{80}+\frac{9^2}{90}\)

               \(A=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}+\frac{5}{10}+\frac{6}{10}+\frac{7}{10}+\frac{8}{10}+\frac{9}{10}\)

             \(A=\frac{45}{10}=\frac{9}{2}\)

            Ủng hộ mk nha !!! ^_^

Ta có: \(\dfrac{1}{5}+\dfrac{4}{10}+\dfrac{9}{15}+\dfrac{16}{20}+\dfrac{25}{25}+\dfrac{36}{30}+\dfrac{49}{35}+\dfrac{64}{40}+\dfrac{81}{45}\)

\(=\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}+\dfrac{5}{5}+\dfrac{6}{5}+\dfrac{7}{5}+\dfrac{8}{5}+\dfrac{9}{5}\)

\(=\dfrac{45}{5}=9\)

\(\dfrac{1}{5}+\dfrac{4}{10}+\dfrac{9}{15}+...+\dfrac{81}{45}\\ =\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+...+\dfrac{9}{15}\\ =\dfrac{\left(1+2+3+...+9\right)}{15}=\dfrac{\left(1+9\right)x9:2}{15}\\ =\dfrac{10x9:2}{15}=\dfrac{45}{15}=3\)