Question

Answer 1

a: \(A=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+....+\dfrac{1}{73}-\dfrac{1}{76}=\dfrac{18}{76}=\dfrac{9}{38}\)

b: \(I=4\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{73}-\dfrac{1}{76}\right)\)

\(=4\cdot\dfrac{19-1}{76}=\dfrac{18}{19}\)

c: \(K=\dfrac{5}{3}\left(\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{73\cdot76}\right)\)

\(=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{73}-\dfrac{1}{76}\right)\)

\(=\dfrac{5}{3}\cdot\dfrac{18}{76}=\dfrac{30}{76}=\dfrac{15}{38}\)