Question

Ajutor rapid, va rog!

Answer 1

Răspuns:

c)   $\frac{(n+1)!-1}{(n+1)!}$

Explicație pas cu pas:

(vezi poza)

Answer 2

Răspuns:

Explicație pas cu pas:

$S_n=...=\dfrac{1}{3}*(\dfrac{1}{1}-\dfrac{1}{4})+\dfrac{1}{3}*(\dfrac{1}{4}-\dfrac{1}{7})+...+\dfrac{1}{3}*(\dfrac{1}{3n-2}-\dfrac{1}{3n+1})=\dfrac{1}{3}*(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{3n-2}-\dfrac{1}{3n+1})=\dfrac{1}{3} *(\dfrac{1}{1}- \dfrac{1}{3n+1} )=\dfrac{1}{3}*\dfrac{3n+1-1}{3n+1} =\dfrac{n}{3n+1}$