I was able to solve (e), this is the only one I don't get.

Determine whether the series is convergent or divergent and say what test you used to solve it.

(d) sum n=1 to infinity
(5n)^(3n) / (5^n + 3)^n

3 answers

Tn = (5n)^(3n) / (5^n + 3)^n
Tn+1 = (5(n+1))^(3(n+1)) / (5^(n+1) + 3)^(n)

Tn+1/Tn = (5(n+1))^(3(n+1)) / (5^(n+1) + 3)^(n+1) * (5^n + 3)^n / (5n)^(3n)

As n->oo, 5^n+3 is just 5^n, so we can simplify things a bit to

(5n)^(3n) * (5n)^3 * 5^(n^2)
----------------------------- =
(5n)^(3n) * 5^n * 5(n^2)

(5n)^3 / 5^n

Since exponentials grow faster than powers, the ratio is less than 1, so the series converges absolutely.
what does Tn stand for?
nth Term of sequence
I thought it would be clear from the context and the obvious use of the ratio test.
Similar Questions
  1. 2. Determine the amplitude of:y= cos x 3. Determine the domain of: y= 4 sin x 4. Determine the range of: y= - sin x 5. Determine
    1. answers icon 1 answer
  2. Need help please. Thank you.1. Determine whether the function has a maximum or minimum. State that value. f(x)= -2x^2-4x 2.
    1. answers icon 2 answers
  3. Solve by eliminnation methods2x-4y=5 2x-4y=6 solve the system by elimination method 5x+2y= -13 7x-3y=17 Solve x+6<-7 or x+6>4
    1. answers icon 1 answer
  4. 1. -2x - 9 = 15 (solve for x)2. 16 - ¾(x) = 10 (solve for x) 3. Solve for x to determine if the equation has one, none, or
    1. answers icon 1 answer
more similar questions