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Very quick question

  • Thread starter jack.o
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Is (3n+3)!=(3n)!+3!
? probably obvious but i'm not certain. Trying to work out a radius of convergence for a series.
 
Is (3n+3)!=(3n)!+3!
? probably obvious but i'm not certain. Trying to work out a radius of convergence for a series.
No. It is the product from i=1 to 3 of (3n!)*(3n+i)
 

nicksauce

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You can quickly verify this for yourself by checking the case where n = 1.
 
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(3n+3)!=(3n+3)(3n+2)(3n+1)(3n)(3n-1)....(6)(5)(4)(3)(2)(1)
 
3
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Ok, this convergence question still has me stuck

[tex]\stackrel{\infty}{\stackrel{\sum}{n=0}}[/tex][tex]\stackrel{\chi^{n}}{\overline{(3n)!}}[/tex]

Got the n+1 term and tried dividing the nth term by the nth+1 but does not seem to cancel nicely.
 
Last edited:

HallsofIvy

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If [tex]\stackrel{\chi^{n}}{(3n)!}[/tex] is not a fraction with the line missing, then I have no idea what you mean.
 
3
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It is meant to be a fraction, not used to the equation editor software here.
 
11
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Jack - you were on the right track by figuring out the n+1 term. Use the ratio test. You should see fairly readily that the series converges to 0 as n goes to infinity.
 

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