Thread: Sequences Questions (2)

Two questions for y'all; both involve determining convergence or divergence, if convergence finding limit:

1) a(sub n) = SQRT((n+1)/(9n+1)): I see that you can make that (N+1)^1/2 divided by (9n + 1)^1/2, but can't progress.

2) a(sub n) = ((-1)^n*n^3)/(n^3+2n^2+1): Since there is the -1^n term, is this simply divergent? Or am I looking at it the wrong way?

Cheers!

Originally Posted by Sprintz

Two questions for y'all; both involve determining convergence or divergence, if convergence finding limit:

1) a(sub n) = SQRT((n+1)/(9n+1)): I see that you can make that (N+1)^1/2 divided by (9n + 1)^1/2, but can't progress.

2) a(sub n) = ((-1)^n*n^3)/(n^3+2n^2+1): Since there is the -1^n term, is this simply divergent? Or am I looking at it the wrong way?

Cheers!

1)

First lets factor out the highest power of n from both the numerator and denominator to get



and reduce to get



Now as so we get



Your are correct that the 2nd sequence diverges, but try an analysis similar to the one I just did. Good luck.