# Very quick question

#### 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.

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#### 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

Homework Helper
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.

Last edited:

#### HallsofIvy

Homework Helper
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.

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