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Question-213642




Question Number 213642 by universe last updated on 12/Nov/24
Answered by Berbere last updated on 12/Nov/24
a_n =lim_(N→∞) Σ_(k=n) ^N (1/k^2 );∀k≥n>1  k(k−1) ≤k^2 ≤k(k+1)⇒  lim_(N→∞) Σ_(k=n) ^N (1/(k(k−1)))≥_ a_n ≥Σ_(k=n) ^∞ (1/(k(k+1)))=Σ_(k=n) ^∞ (1/k)−(1/(k+1))=(1/n)  (1/(n−1))≥a_n ≥(1/n)⇒lim_(n→∞) n.a_n =1  n^2 a_n ≥n⇒lim_(n→∞)  n^2 a_n =+∞
an=limNNk=n1k2;kn>1k(k1)k2k(k+1)limNNk=n1k(k1)ank=n1k(k+1)=k=n1k1k+1=1n1n1an1nlimnn.an=1n2annlimnn2an=+
Commented by universe last updated on 12/Nov/24
thank you so much sir
thankyousomuchsir

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