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Does #a_n=(n + (n/2))^(1/n) # converge?

1 Answer

Nov 28, 2016

The sequence is convergent.

Explanation:

#a_n=(n+n/2)^(1/n)=n^(1/n)(3/2)^(1/n)#
so
#lim_(n->oo)(n+n/2)^(1/n)=lim_(n->oo)n^(1/n)lim_(n->oo)(3/2)^(1/n)#

but #lim_(n->oo)n^(1/n)=1# and #lim_(n->oo)(3/2)^(1/n)=1#

so

#lim_(n->oo)a_n=1# and the sequence converges.

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