a: \(=\dfrac{1}{3}-\dfrac{37}{100}+\dfrac{1}{8}-\dfrac{32}{25}+\dfrac{-5}{2}+\dfrac{3}{2}\)

\(=\dfrac{1}{3}+\dfrac{1}{8}-1-\dfrac{37}{100}-\dfrac{128}{100}\)

\(=\dfrac{8+3-24}{24}-\dfrac{165}{100}\)

\(=\dfrac{-263}{120}\)

b: \(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)

\(=\dfrac{5}{22}-\dfrac{4}{22}-\dfrac{13}{8}+\dfrac{12}{8}+\dfrac{3}{13}\)

\(=\dfrac{1}{22}-\dfrac{1}{8}+\dfrac{3}{13}=\dfrac{173}{1144}\)

a: \(=\dfrac{1}{3}-\dfrac{37}{100}+\dfrac{1}{8}-\dfrac{32}{25}-\dfrac{5}{2}+\dfrac{3}{2}\)

\(=\dfrac{11}{24}+\left(-\dfrac{37}{100}+\dfrac{1}{8}-1\right)\)

\(=\dfrac{11}{24}-\dfrac{249}{200}=-\dfrac{59}{75}\)

b: \(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)

\(=\dfrac{5}{22}-\dfrac{4}{22}+\dfrac{3}{13}-\dfrac{13}{8}+\dfrac{12}{8}\)

\(=\dfrac{1}{22}+\dfrac{3}{13}-\dfrac{1}{8}=\dfrac{173}{1144}\)

\(=\dfrac{1}{2}-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{1}{2016}=\dfrac{1}{2016}\)

A = 2 x 100 - 2 x 99 + 2 x 98 - 2 x 97 + ... + 2 x 2 - 2x 1

Xét dãy số: 1; 2;...;97; 98; 99; 100

Dãy số trên có 100 số hạng. Vì 100 : 2 = 50

Nhóm hai số hạng liên tiếp của a vào một nhóm khi đó ta có:

A = (2 x 100 - 2 x 99) + (2 x 98 - 2 x 97) +...+(2x2 - 2 x1)

A = 2 x (100 - 99) + 2 x (98 - 97) + ...+ 2 x (2 - 1)

A = 2 x 1 + 2 x 1 + ... + 2 x 1

A = 2 + 2 + ... + 2

A = 2 x 50

A = 100