Question

Demonstrati ca sirul $(a_n)_(_n_\geq_1_) , unde, an=\frac{n+1}{n^2}$ este marginit.

Answer 1

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Answer 2

(n+1)/n²>0 ∀n≥1
(n+1)/n²<n²/n²=1 ∀n≥2 deci (n+1)/n²≤1, ∀n≥2 ***
 pt n=1, a1=2

deci (n+1)/n²≤2 ∀n≥1 si
(n+1)/n²>0, ∀n≥1
deci sirul an este marginit 


***
n+1<n²
 f(n) :R->R. n²-n-1>0 pt n>(1+√5)/2 <2