b)Ta có:\(A=1+\frac{1}{2.\left(1+2\right)}+\frac{1}{3.\left(1+2+3\right)}+...+\frac{1}{16.\left(1+2+3+...+16\right)}\)

                 \(=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{16}.\left(1+2+3+...+16\right)\)

                 \(=1+\frac{1}{2}.3+\frac{1}{3}.6+...+\frac{1}{16}.136\)

                 \(=1+1,5+2+...+8,5\)

                 \(=\frac{\left(8,5+1\right).\left[\left(8,5-1\right):0,5+1\right]}{2}=76\)

B=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<\)                                                                               

 B=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

B=\(1-\frac{1}{8}=\frac{8}{8}-\frac{7}{8}=\frac{1}{8}<2\)

Vậy 1/8<2 hay 1/8<16/8

a)\(=\dfrac{16}{13}-\dfrac{3}{15}+\dfrac{6}{13}=\dfrac{22}{13}-\dfrac{3}{15}=\dfrac{96}{65}\)

b)\(=\dfrac{21}{8}-\left(\dfrac{5}{10}+\dfrac{6}{10}\right)=\dfrac{21}{8}-\dfrac{11}{10}=\dfrac{61}{40}\)

c)\(=\dfrac{27}{10}-3-\dfrac{4}{7}--\dfrac{61}{70}\)

d)\(=\dfrac{576}{702}=\dfrac{4}{5}\)

e)\(=\left(\dfrac{20}{15}-\dfrac{12}{15}\right)\times\dfrac{25}{2}=\dfrac{8}{15}\times\dfrac{25}{2}=\dfrac{20}{3}\)

f)\(=\dfrac{24}{12}-\dfrac{4}{12}-\dfrac{6}{12}-\dfrac{2}{12}-\dfrac{3}{12}=\dfrac{9}{12}=\dfrac{3}{4}\)

d) \(=\dfrac{32}{45}x\dfrac{18}{16}=\dfrac{576}{720}=\dfrac{115}{114}\)

e) \(=\left(\dfrac{4}{3}-\dfrac{4}{5}\right)x\dfrac{25}{12}=\dfrac{8}{15}x\dfrac{25}{12}=\dfrac{200}{180}=\dfrac{10}{9}\)

f) \(=\dfrac{2}{1}-\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{3}{12}=\dfrac{24}{12}-\dfrac{4}{12}-\dfrac{6}{12}-\dfrac{2}{12}-\dfrac{3}{12}\)

\(=\dfrac{20}{12}-\dfrac{4}{12}-\dfrac{3}{12}=\dfrac{16}{12}-\dfrac{3}{12}=\dfrac{13}{12}\)

MK ghi sai để mk sửa lại nha

a) \(\frac{-3}{16}+\frac{-7}{16}+\frac{6}{-16}\)

\(=-\frac{3}{16}+-\frac{7}{16}+\frac{-6}{16}\)

\(=\frac{\left(-3\right)+\left(-7\right)+\left(-6\right)}{16}\)

\(=\frac{-16}{16}=-1\)

b) \(\frac{2}{5}-\frac{1}{7}+\frac{7}{10}\)

\(=\frac{28}{70}-\frac{10}{70}+\frac{49}{70}\)

\(=\frac{28-10+49}{70}\)

\(=\frac{67}{70}\)

c) \(3+\frac{1}{3}-2\frac{1}{2}\)

\(=\frac{3}{1}+\frac{1}{3}-\frac{5}{2}\)

\(=\frac{18}{6}+\frac{2}{6}-\frac{15}{6}\)

\(=\frac{18+2-15}{6}\)

\(=\frac{5}{6}\)

d) \(-\frac{3}{5}-\left(-\frac{2}{15}\right)\)

\(=-\frac{3}{5}+\frac{2}{15}\)

\(=\frac{-9}{15}+\frac{2}{15}\)

\(=-\frac{7}{15}\)

\(\frac{-3}{16}\)+(\(\frac{-7}{16}\) ) +(\(\frac{6}{-16}\))

=\(\frac{-3-7-6}{16}\)

=\(\frac{-16}{16}\)= \(-1\)

\(\frac{2}{5}\)\(-\)\(\frac{1}{7}\)+\(\frac{7}{10}\)

=\(\frac{9}{35}\)+\(\frac{7}{10}\)

=\(\frac{67}{70}\)

3+ \(\frac{1}{3}\)\(-\) \(\frac{21}{2}\)

=\(\frac{18+2-63}{6}\)

=\(\frac{-43}{6}\)

\(\frac{-3}{5}\)\(-\)(\(\frac{-2}{15}\))

=\(\frac{-3}{5}\)+\(\frac{2}{15}\)

=\(\frac{-9+2}{15}\)

=\(\frac{-7}{15}\)

\(A=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{16}\left(1+2+3+...+16\right)\\ \Rightarrow A=1+\dfrac{1}{2}\cdot\dfrac{2\cdot3}{2}+\dfrac{1}{3}\cdot\dfrac{3\cdot4}{2}+...+\dfrac{1}{16}\cdot\dfrac{16\cdot17}{2}\\ \Rightarrow A=\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+\dfrac{5}{2}+...+\dfrac{16}{2}+\dfrac{17}{2}\\ \Rightarrow A=\dfrac{1}{2}\left(2+3+4+...+17\right)=76\)