Grade 11Algebra

PROVE THAT (3n)! is divisible by n!(n+1)!(n+2)!.

ARITRA SINHA

14 Years agoGrade 11

3 Answers

Ashwin Muralidharan IIT Madras

14 Years ago

Hi Aritra,

This is not true.

Check that for n=1, n=2....... (3n)! will not be divisible by n!(n+1)!(n+2)!....

This result holds true only for n ≥ 3, and is quite easy to prove.

Use that the product of n-consecutive numbers, is always divisible by n!.

Hope this helps.

Best Regards,

Ashwin (IIT Madras).

jitender lakhanpal

Approved Tutor Answer14 Years ago

Dear aritra,

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

take the terms 3n,3n-3,3n-6,3n-9.....upto 3 and 2n,2n-2,2n-4.........upto 2

together and take 3 common from each and similarly 2 common from each

so we get n! twice and there is one more n! is already present so when we divide n!*(n+1)!*(n+2)!

all the three n! gets cancelled and remaining n+1, n+2 is also present in the equation 1

so n!*(n+1)!*(n+2)! divides 3n! completely ------hence proved

We are all IITians and here to help you in your IIT JEE preparation.

Now you can win by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..

jitender

askiitians expert