Determine whether the following series converges: sum_(k = 1)^oo (2/(k + 5)^3

pedzenekO 2021-08-20 Answered
Determine whether the following series converges: \(\displaystyle{\sum_{{{k}={1}}}^{\infty}}{\left(\frac{{2}}{{\left({k}+{5}\right)}^{{3}}}\right)}\).

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

hesgidiauE
Answered 2021-08-21 Author has 16917 answers
\(\displaystyle{\sum_{{{k}={1}}}^{\infty}}{\left(\frac{{2}}{{\left({k}+{5}\right)}^{{3}}}\right)}\)
\(\displaystyle\lim_{{{k}\to\infty}}{\left({a}_{{k}}\right)}=\lim_{{{\left({k}\to{5}\right)}^{{5}}}}{\left(\frac{{2}}{{\left({k}+{5}\right)}^{{3}}}\right)}=\frac{{9}}{\infty}={0}\)
The limit of the terms of the series is 0, so the series diverges by the divergent test.
Have a similar question?
Ask An Expert
15
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...