How to calculate the limit $lim_ntoinftysqrtn^2+3n-n$? [on hold]

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Given
$$a_n=sqrtn^2+3n-n$$
how can I calculate
$$
lim_ntoinftya_n ?
$$



I tried rationalizing, but got nowhere.






sequences-and-series limits radicals







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put on hold as off-topic by xbh, Key Flex, amWhy, Theoretical Economist, Hans Lundmark yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – xbh, Key Flex, amWhy, Theoretical Economist
If this question can be reworded to fit the rules in the help center, please edit the question.












  • A better way to post is to show how you did the rationalization and explain why you thought you could go nowhere. These things would make your post easy to be accepted and to receive more advices to help you.
    – xbh
    yesterday










  • Possible duplicate of Limits: How to evaluate $limlimits_xrightarrow inftysqrt[n]x^n+a_n-1x^n-1+cdots+a_0-x$
    – Hans Lundmark
    yesterday














up vote
0
down vote

favorite
1












Given
$$a_n=sqrtn^2+3n-n$$
how can I calculate
$$
lim_ntoinftya_n ?
$$



I tried rationalizing, but got nowhere.






sequences-and-series limits radicals







share|cite|improve this question















put on hold as off-topic by xbh, Key Flex, amWhy, Theoretical Economist, Hans Lundmark yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – xbh, Key Flex, amWhy, Theoretical Economist
If this question can be reworded to fit the rules in the help center, please edit the question.












  • A better way to post is to show how you did the rationalization and explain why you thought you could go nowhere. These things would make your post easy to be accepted and to receive more advices to help you.
    – xbh
    yesterday










  • Possible duplicate of Limits: How to evaluate $limlimits_xrightarrow inftysqrt[n]x^n+a_n-1x^n-1+cdots+a_0-x$
    – Hans Lundmark
    yesterday












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





Given
$$a_n=sqrtn^2+3n-n$$
how can I calculate
$$
lim_ntoinftya_n ?
$$



I tried rationalizing, but got nowhere.






sequences-and-series limits radicals







share|cite|improve this question















Given
$$a_n=sqrtn^2+3n-n$$
how can I calculate
$$
lim_ntoinftya_n ?
$$



I tried rationalizing, but got nowhere.






sequences-and-series limits radicals




sequences-and-series limits radicals






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited yesterday









AccidentalFourierTransform

1,341627




1,341627










asked yesterday









Bili Debili

1348




1348




put on hold as off-topic by xbh, Key Flex, amWhy, Theoretical Economist, Hans Lundmark yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – xbh, Key Flex, amWhy, Theoretical Economist
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by xbh, Key Flex, amWhy, Theoretical Economist, Hans Lundmark yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – xbh, Key Flex, amWhy, Theoretical Economist
If this question can be reworded to fit the rules in the help center, please edit the question.











  • A better way to post is to show how you did the rationalization and explain why you thought you could go nowhere. These things would make your post easy to be accepted and to receive more advices to help you.
    – xbh
    yesterday










  • Possible duplicate of Limits: How to evaluate $limlimits_xrightarrow inftysqrt[n]x^n+a_n-1x^n-1+cdots+a_0-x$
    – Hans Lundmark
    yesterday
















  • A better way to post is to show how you did the rationalization and explain why you thought you could go nowhere. These things would make your post easy to be accepted and to receive more advices to help you.
    – xbh
    yesterday










  • Possible duplicate of Limits: How to evaluate $limlimits_xrightarrow inftysqrt[n]x^n+a_n-1x^n-1+cdots+a_0-x$
    – Hans Lundmark
    yesterday















A better way to post is to show how you did the rationalization and explain why you thought you could go nowhere. These things would make your post easy to be accepted and to receive more advices to help you.
– xbh
yesterday




A better way to post is to show how you did the rationalization and explain why you thought you could go nowhere. These things would make your post easy to be accepted and to receive more advices to help you.
– xbh
yesterday












Possible duplicate of Limits: How to evaluate $limlimits_xrightarrow inftysqrt[n]x^n+a_n-1x^n-1+cdots+a_0-x$
– Hans Lundmark
yesterday




Possible duplicate of Limits: How to evaluate $limlimits_xrightarrow inftysqrt[n]x^n+a_n-1x^n-1+cdots+a_0-x$
– Hans Lundmark
yesterday










1 Answer
1






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up vote
6
down vote



accepted










$$a_n = sqrtn^2+3n-n = frac3nsqrtn^2+3n+n = frac3sqrt1+3n^-1+1 to frac3sqrt1+1 = frac32$$






share|cite|improve this answer



























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    6
    down vote



    accepted










    $$a_n = sqrtn^2+3n-n = frac3nsqrtn^2+3n+n = frac3sqrt1+3n^-1+1 to frac3sqrt1+1 = frac32$$






    share|cite|improve this answer
























      up vote
      6
      down vote



      accepted










      $$a_n = sqrtn^2+3n-n = frac3nsqrtn^2+3n+n = frac3sqrt1+3n^-1+1 to frac3sqrt1+1 = frac32$$






      share|cite|improve this answer






















        up vote
        6
        down vote



        accepted







        up vote
        6
        down vote



        accepted






        $$a_n = sqrtn^2+3n-n = frac3nsqrtn^2+3n+n = frac3sqrt1+3n^-1+1 to frac3sqrt1+1 = frac32$$






        share|cite|improve this answer












        $$a_n = sqrtn^2+3n-n = frac3nsqrtn^2+3n+n = frac3sqrt1+3n^-1+1 to frac3sqrt1+1 = frac32$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered yesterday









        Kenny Lau

        19.1k2158




        19.1k2158












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