Using the definition of convergence, how do you prove that the sequence # lim (3n+1)/(2n+5)=3/2# converges?

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Using the definition of convergence, how do you prove that the sequence # lim (3n+1)/(2n+5)=3/2# converges?

1 Answer

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Answer 1 · 2016-06-06T15:53:57

I assume meant limit at infinity, that is, to show that #lim_(n->infty) (3n+1)/(2n+5) = 3/2#. Note that #lim_(n->infty)1/n = 0# and similarly #lim_(n->infty)k/n = 0# for any real, positive #k#.

Explanation:

Also note that by dividing by #n# on both numerator and denominator, #(3n+1)/(2n+5) = (3+1/n)/(2+5/n)#

This means that #lim_(n->infty) (3n+1)/(2n+5) = lim_(n->infty) (3+1/n)/(2+5/n) = (3+0)/(2+0) = 3/2#

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Using the definition of convergence, how do you prove that the sequence # lim (3n+1)/(2n+5)=3/2# converges?

1 Answer

Explanation:

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