Determine the radius of convergence of the series <munderover> &#x2211;<!-- ∑ --> <mrow c

gnatopoditw

gnatopoditw

Answered question

2022-06-20

Determine the radius of convergence of the series n = 1 a n z n where a n = n 2 4 n + 3 n

Answer & Explanation

grcalia1

grcalia1

Beginner2022-06-21Added 23 answers

You have
a n = 4 n n 2 1 + 3 n 4 n ,
and therefore
lim n a n n = lim n 1 4 n 2 1 + 3 n 4 n n = lim n 1 4 n n 2 1 + 3 n 4 n n = 1 4 .
Therefore, the radius of convergence is 4

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