This sequence converge or diverge 2/5,1/2,6/11,4/7,.....?

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Answer 1 · 2018-04-17T20:42:22

#lim_(n->oo) (2n)/(3n+2) = 2/3#

Given:

#2/5, 1/2, 6/11, 4/7,...#

Without extra information (e.g. telling us what kind of sequence), no finite initial sequence determines what follows.

That having been said, we can see a pattern here, by rewriting the given sequence as:

#2/5, 4/8, 6/11, 8/14,..., (2n)/(3n+2), ...#

Then we find:

#lim_(n->oo) (2n)/(3n+2) = lim_(n->oo) 2/(3+2/n) = 2/3#