\(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + ... + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\)

=\(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + ... + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)

=\(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + ... + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\)

=\(\dfrac{1}{1}\) - \(\dfrac{1}{7}\)

=\(\dfrac{6}{7}\)

Thank you. You are very good