Question

Cum se calculează 4/5+4/45+4/117+...+4/2017×2021?

Answer 1

[tex]Forma\ generala:\frac{4}{n(n+4)}=\frac{n+4-n}{n(n+4)}=\frac{1}{n}-\frac{1}{n+4}\\ Revenind:\\ \frac{4}{1\cdot 5}+\frac{4}{5\cdot 9}+\frac{4}{9\cdot 13}+...+\frac{4}{2017\cdot 2021}=\\ 1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{2017}-\frac{1}{2021}=\\ Termenii\ se\ reduc\ si\ mai\ ramane:\\ 1-\frac{1}{2021}=\frac{2020}{2021}[/tex]