Question

Convergence, divergence

Answer 1

Determine if each series is a convergent series or a divergent series.

Answer 2

Would you use a root test, ratio test or integral test for this?

Answer 3

I was trying ratio test

Answer 4

but my cat took my ink pen

Answer 5

i got it back

Answer 6

Haha, Hi freckles

Answer 7

under what circumstance would you use an integral test

Answer 8

i would never use integral test if I had a factorial or alternating series

Answer 9

it would have to be something I could at least integrate

Answer 10

true XD makes sense

Answer 11

root test also doesn't sound right either

Answer 12

because of the factorial business

Answer 13

i have you tried ratio test

Answer 14

crap seriously she keeps taking my pen

Answer 15

\[\lim_{n \rightarrow \infty}| \frac{(n+1)!}{(n+1)^{n+1}} \frac{n^n}{n!}|\]

Answer 16

I'm working on it right now

Answer 17

how would you simplify the n^n/(n+1)^n+1 part

Answer 18

this is the way i'm approaching it so far
\[\lim_{n \rightarrow \infty}| \frac{(n+1)!}{(n+1)^{n+1}} \frac{n^n}{n!}| \\ = \lim_{n \rightarrow \infty}|\frac{n+1}{(n+1)^{n}(n+1)} n^n| \\ =\lim_{n \rightarrow \infty}|(\frac{n}{n+1})^n|\]
\[=\lim_{n \rightarrow \infty}|e^{\ln((\frac{n}{n+1})^n)}|=\lim_{n \rightarrow \infty}|e^{n \ln(\frac{n}{n+1})}| \\ = \lim_{n \rightarrow \infty} | e^{\frac{\ln(\frac{n}{n+1})}{\frac{1}{n}}}| \]

Answer 19

for line 2 how did you move the ^n+1

Answer 20

\[x^{2}=x^{1+1}=x^1 x^1\\x^{n+1}=x^{n}x^{1}\]

Answer 21

law of exponents

Answer 22

\[x^rx^s=x^{r+s}\]