M = - \(\frac{4}{1.5}\) - \(\frac{4}{5.9}\) - ... - \(\frac{4}{n\left(n+4\right)}\)
= - (\(\frac{4}{1.5}\) + \(\frac{4}{5.9}\) + ... + \(\frac{4}{n\left(n+4\right)}\)
= - ( 1 - \(\frac{1}{5}\) + \(\frac{1}{5}\) - \(\frac{1}{9}\) + ... + \(\)\(\frac{1}{n}\) - \(\frac{1}{n+4}\)
= - ( 1 - \(\frac{1}{n+4}\))
= - \(\frac{n+3}{n+4}\)