Question

Does this diverge or converge?

∑(n = 1, ∞) (( -7)^n)/(n^(6n^3)+(3^n)

Does this diverge or converge?
∑(n = 1, ∞) 9/(3n+7(square root of n)

Answer 1

i can't read the first one
the second one looks like
\[\sum_{n=1}^{\infty}\frac{9}{3n+7\sqrt{n}}\]

Answer 2

yes second one is correct
i'll rewrite the first just one second

Answer 3

the second one diverges for sure, because the degree of the denominator is 1, and the degree of the numerators is 0 and in order for it to converge the degree of the bottom has to be larger than the degree of the top by more than one

Answer 4

if you have to please your math teacher, you can use the "limit comparison test" and compare it to the well known divergent series
\[\sum\frac{1}{n}\]

Answer 5

here is the second
∑(n = 1, ∞) ( -7)^n / (n^(6n)^3 +(3)^n

Answer 6

the comparison test?

Answer 7

i still can't read it
but it looks like it alternates
if it alternates, all you have to check for convergence is that the terms are decreasing and go to zero

Answer 8

oh I see what your saying, could I use the comparison test for the second question?

Answer 9

sorry i meant the first?

Answer 10

for the second one, compare to
\[\sum\frac{1}{n}\] which you know converges

Answer 11

i mean for this one
\[\sum_{n=1}^{\infty}\frac{9}{3n+7\sqrt{n}}\]

Answer 12

but you have to use the limit comparison test, not the regular comparison test

Answer 13

the first one i still can't get
but it does alternate
as long as the terms go to zero, it converges