Question

.8 Give an example of a sequence ($a_n$) of real numbers with the following properties. (i) ($a_n$) is not convergent; (ii) for each $k \ge 2$ the subsequence ($a_{kn}$)$_{n=1}^{\infty}$ is convergent. (Split your definition of $a_n$ into two cases---one when $n$ is prime, the other when $n$ is composite.)

          .8 Give an example of a sequence ($a_n$) of real numbers with the following properties.
(i) ($a_n$) is not convergent;
(ii) for each $k \ge 2$ the subsequence ($a_{kn}$)$_{n=1}^{\infty}$ is convergent.
(Split your definition of $a_n$ into two cases---one when $n$ is prime, the other when $n$ is composite.)

.8 Give an example of a sequence (an) of real numbers with the following properties.
(i) (an) is not convergent;
(ii) for each k ≥ 2 the subsequence (akn)n=1^∞ is convergent.
(Split your definition of an into two cases—one when n is prime, the other when n is composite.)

Added by Craig H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nick Johnson

09/01/2021

Step 1

Step 1: Define the sequence (an) for prime n: Let's define the sequence (an) for prime n as follows: For prime n, let an = n. Show more…

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.8Give an example of a sequence (an) of real numbers with the followingproperties.(i) (a) is not convergent;(i) for each k>2 the subsequence (akn) is convergent.(Split your definition of an into two cases-one when n is prime, theother when n is composite.) .8 Give an example of a sequence (an) of real numbers with the following properties. (i) (an) is not convergent; (ii) for each k 2 the subsequence (akn)n=1 is convergent. (Split your definition of an into two cases--one when n is prime, the other when n is composite.)