Question

summation 1 to infinity -> n!/(n!+1)
convergent or divergent

Answer 1

\[\sum_{1}^{\infty} n!/(n!+1)\]

Answer 2

not sure how to break down the factorials

Answer 3

all it is asking is to use the limit approaching infinity of a_n and see if divergent or needs further testing (which means it approaches 0)

Answer 4

well \[\large \lim_{n \to \infty} \frac{n!}{n!+1}=1 \]

Answer 5

how did you do the factorials?

Answer 6

can you just divide top and bottom by 1/n!

Answer 7

\[\large \lim_{n \to \infty} \frac{n!}{n!+1}= \lim_{n \to \infty} \frac{n!}{n!(1+ \frac{1}{n!})}= \lim_{n \to \infty} \frac{1}{1+ \frac{1}{n!}} \]

Answer 8

\(a_n\) does not converge to zero, thus the series can't converge, the series is divergent.

Answer 9

ahhh ok that makes sense

Answer 10

thank you very much

Answer 11

You're very welcome.