Question

Answer 1

a: \(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}=\dfrac{1}{2}-\dfrac{1}{8}=\dfrac{3}{8}\)

b: \(=\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+...+\dfrac{1}{12}-\dfrac{1}{13}=\dfrac{1}{7}-\dfrac{1}{13}=\dfrac{6}{91}\)

c: \(=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+...+\dfrac{1}{13\cdot16}+\dfrac{1}{16\cdot19}\)

=1/3(1-1/4+1/4-1/7+...+1/16-1/19)

=1/3*18/19

=6/19