Limit of sequence to infinity. For a sequence {a_n}, given that the value of sum_{n=1}^{infty}(a_n^2+4na_n+4n^2)=4 what is the value of lim_{n rightarrow infty} (a_n)/n

Taylor Barron

Taylor Barron

Answered question

2022-11-11

Limit of sequence to infinity
For a sequence { a n }, given that the value of
n   =   1 ( a n 2 + 4 n a n + 4 n 2 ) = 4
what is the value of
lim n a n n

Answer & Explanation

metodikkf6z

metodikkf6z

Beginner2022-11-12Added 14 answers

Step 1
Note that
n = 1 ( a n 2 + 4 n a n + 4 n 2 ) = n = 1 ( a n + 2 n ) 2 .
Step 2
So as the series converges, then necessarily ( a n + 2 n ) 2 0, and thus a n + 2 n n 0, also. Hence
a n n 2.

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