Question

Calculati:
1/5×6+1/6×7+...+1/15×16+1/16×17​

Answer 1

Răspuns:

Explicație pas cu pas:

se arat rapid aca 1/(n(n+1))=1/n-1/(n+1)

atunci suma devine

1/5-1/6+1/6-1/7+...+1/16-1/17=

=1/5-1/17

=17/85-5/85=12/85

Answer 2

$\it \dfrac{1}{n(n+1)}=\dfrac{1}{n}-\dfrac{1}{n+1}\ \ \ \ \ (*)\\ \\ \\ Folosind\ rela\c{\it t}ia\ (*),\ suma\ devine:\\ \\ \\ S=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\ ...\ +\dfrac{1}{16}-\dfrac{16}{17}=\dfrac{^{17)}1}{\ \ 5}-\dfrac{^{5)}1}{\ 17}=\dfrac{12}{85}$