Friday, 2 September 2016

limits - limnrightarrowinftyan=+infty,limnrightarrowinftybn=+infty and limnrightarrowinfty(an+bn)=infty.



Give an example limnan=+,limnbn=+ and limn(an+bn)=.




I think it's impossible, but my teacher says it's real


Answer



If limnan=+ and limnbn=+, then there is NN such that



an,bn>0 for n>N. Therefore an+bn>0 for n>N.



Hence we can not have that limn(an+bn)=.


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