anonymous
  • anonymous
8. Test the series for convergence or divergence: summantion (n= infinite to1)[n!/(2.5.8..............(3n+2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Zarkon
  • Zarkon
ratio test
anonymous
  • anonymous
\[\sum_{n=1}^{\infty}(n!/2.5.8..................(3n+2))\] its like this
Zarkon
  • Zarkon
ok...use the ratio test

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anonymous
  • anonymous
but how?
Zarkon
  • Zarkon
compute \[\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|\]
anonymous
  • anonymous
can you show me all steps please :(
Zarkon
  • Zarkon
all of them...hmmm...I'm pretty lazy...I'll just get you started
Zarkon
  • Zarkon
\[a_n=\frac{n!}{2\cdot5\cdot8\cdots(3n+2)}\]
Zarkon
  • Zarkon
\[\frac{a_n+1}{a_n}=\frac{\frac{(n+1)!}{2\cdot5\cdot8\cdots(3(n+1)+2)}}{\frac{n!}{2\cdot5\cdot8\cdots(3n+2)}}\]
Zarkon
  • Zarkon
\[=\frac{n+1}{3(n+1)+2}\]
Zarkon
  • Zarkon
take limit
anonymous
  • anonymous
love you for this :))
anonymous
  • anonymous
next ?
Zarkon
  • Zarkon
did you find the limt

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