Radius of Convergence for Series: 3n+3 vs 3n+3!

[jack.o]

Is (3n+3)!=(3n)!+3!
? probably obvious but I'm not certain. Trying to work out a radius of convergence for a series.

 

[John Creighto]

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]

You can quickly verify this for yourself by checking the case where n = 1.

 

[Feldoh]

(3n+3)!=(3n+3)(3n+2)(3n+1)(3n)(3n-1)...(6)(5)(4)(3)(2)(1)

 

[jack.o]

Ok, this convergence question still has me stuck

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

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

 

[HallsofIvy]

If \stackrel{\chi^{n}}{(3n)!} is not a fraction with the line missing, then I have no idea what you mean.

 

[jack.o]

It is meant to be a fraction, not used to the equation editor software here.

 

[driscoll79]

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.