Question

8. Test the series for convergence or divergence:
summantion (n= infinite to1)[n!/(2.5.8..............(3n+2)

Answer 1

ratio test

Answer 2

\[\sum_{n=1}^{\infty}(n!/2.5.8..................(3n+2))\] its like this

Answer 3

ok...use the ratio test

Answer 4

but how?

Answer 5

compute

\[\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|\]

Answer 6

can you show me all steps please :(

Answer 7

all of them...hmmm...I'm pretty lazy...I'll just get you started

Answer 8

\[a_n=\frac{n!}{2\cdot5\cdot8\cdots(3n+2)}\]

Answer 9

\[\frac{a_n+1}{a_n}=\frac{\frac{(n+1)!}{2\cdot5\cdot8\cdots(3(n+1)+2)}}{\frac{n!}{2\cdot5\cdot8\cdots(3n+2)}}\]

Answer 10

\[=\frac{n+1}{3(n+1)+2}\]

Answer 11

take limit

Answer 12

love you for this :))

Answer 13

next ?

Answer 14

did you find the limt