Question

Test for convergence or divergence:

n^2+1/(n^3+1)
I know that this is easy but wanted to make sure I was doing this correctly.
I wanted to use direct comparison test:
I chose (n^2)/(n^3)...which simplifies to (1/n)...as my (bsubn) and the original problem as my (asubn). (bsubn) is divergent and smaller than (asubn) so the series would be divergent, which I believe is what the answer is. Am I right though?

Answer 1

yes

Answer 2

no

Answer 3

you need to show its less.

Answer 4

the easiest thing to say is that the differences in the degrees is one
if it is going to converge the degree of the denominator must be more than one larger than the degree of the numerator

Answer 5

my book says that if (bsubn) is divergent, and (asubn) is less than (bsubn) for all n, then (asubn) is also divergent.

Answer 6

so what would be my two comparisons?

Answer 7

a_n is positive...

Answer 8

Im checking my book and it says its Divergent..

Answer 9

What you did first was just fine from what I can see. The only super slight error is that if 1/n is the lower of the two, you technically make it a sub n : )

Answer 10

I guess I was just waiting to see what other people would say. But what you did made perfect sense. Your original series, eliminating the needless constants, resembles 1/n, so that would be your comparison series. 1/n is always less than your original, so the seriesis divergent.

Answer 11

Thanks Psymon.

Answer 12

THanks zzrockr for your help too

Answer 13

Of course. I need to review these things myself anyway, always worth a look : )