For a sequence An, find a number r such that

Question

limit as n approaches infinity of (An/r^n) is a finite non-zero number.

r = ______________.

Answer 1

As n gets larger the only terms which make a significant contribution are the terms with n in the exponent.

For notational convenience write 19^-60 as C and 3^.8/19 = .126749 as p, then a_n approaches Cp⁶ⁿ .

Since p is less than 1 this limit goes to zero as n increases.

If a_n is divided by p⁶ⁿ then the sequence approaches C as a limit.

Therefore, then answer to this question is r=p⁶.