Question

Let (sn) be a sequence defined by sn = n^2(-1)^n. How do you express the subsequence comprised of the positive elements of the sequence?

Answer 1

To express the subsequence comprised of the positive elements of the given sequence, we can consider the values of n when the terms are positive (even values of n) and express them as n^2. Similarly, for the negative elements, we can consider the odd values of n and express them as -n^2.

Step-by-step explanation:

The sequence defined by sn = n2(-1)n is a combination of positive and negative elements. To express the subsequence comprised of the positive elements, we need to consider the values of n for which sn is positive.

When n is even, the term sn is positive because (-1)n = 1. So, the subsequence when n is even is sn = n2.

When n is odd, the term sn is negative because (-1)n = -1. So, the subsequence when n is odd is sn = -n2.