Tuesday, January 19, 2016

calculus - What is the limit of the sequence (frac34n1+n)(1+frac1n)n?



I am trying to find the limit of the sequence
(34n1+n)(1+1n)n
I am aware that if one sequence converges and another sequence converges then the multiplication of two sequences also converge. The limit of the first sequence is 4. However I do not know how to calculate the limit of the second sequence.



Answer



Here is one approach
(1+1n)n=enln(1+1n)=en(1n12n2+)=e112n+e


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