What will be the limit of the following sequence as n tends to infinity? Will the sequence converge or diverge?

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What will be the limit of the following sequence as n tends to infinity? Will the sequence converge or diverge?

#lim_(n rarr oo)a_n# where #a_n= (1+sinn)^(1/n) #

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"

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Answer 1 · 2018-02-24T15:06:38

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Explanation:

#lim_(n→∞)a_n=lim_(n→∞)(1+sinn)^(1/n)#
#=(1+sin∞)^(1/∞)#
#=(1+#(any number between -1 and 1)#)^0#
#=1#
this implies that given sequence convergent and it converges to 1

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What will be the limit of the following sequence as n tends to infinity? Will the sequence converge or diverge?

#lim_(n rarr oo)a_n# where #a_n= (1+sinn)^(1/n) #

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Explanation:

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