Explicație pas cu pas:
a)
[tex]\frac{1}{n} - \frac{1}{n + 1} = \frac{n + 1}{n(n + 1)} - \frac{n}{n(n + 1)} = \frac{n + 1 - n}{n(n + 1)} = \\ = \red{\bf \frac{1}{n(n + 1)}} \\ [/tex]
b)
[tex]\frac{1}{1\cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + ... + \frac{1}{2017 \cdot 2018} + \frac{1}{2018 \cdot 2019} + \frac{1}{2019 \cdot 2020} \\[/tex]
[tex]= \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{2017} - \frac{1}{2018} + \frac{1}{2018} - \frac{1}{2019} + \frac{1}{2019} - \frac{1}{2020} \\[/tex]
[tex]= \frac{1}{1} - \frac{1}{2020} = \frac{2020 - 1}{2020} = \red{\bf \frac{2019}{2020}} \\ [/tex]
