Friday, August 17, 2018

calculus - limntoinftyn3(frac34)n




I have the sequence an=(n3)(34)n
and I need to find whether it converges or not and the limit.




I took the common ratio which is 3(n+1)34n3 and since |34|<1 it converges.
I don't know how to find the limit from here.


Answer



If an+1anl with |l|<1 then an0. (In fact the series an converges).



In this case an+1an=(1+1n)3(34)34.


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