Number of terms

[sarathsasikumar]

General question :

How do you find the number of terms in(a1+a2+a3....an)^m ?

[jssaggu.tico]

This question is out of scope as per GMAT is concerned.
But, if you still need answer, let me know.
I promise that it will take forever to digest it because of huge series of summation gets formed with lot of variables with explanation.

Best Regards

[sarathsasikumar]

Let me throw some specifics in - How to you find the number of terms in say (a+b+c)^50 ?

[jssaggu.tico]

Considering this (a+b+c)^50.

By binomial theorem, we know that (a+b)^n has n+1 terms.
Now in our case lets consider 'b+c' as B'.
Then we have, (a+B')^50 which has 50+1 terms and out of these 50 terms are dependent on B'. So those 50 terms further will be like (b+c), (b+c)^2, (b+c)^3.......................(b+c)^50.

So we have total number of terms as 1+(1+1)+(2+1)...............(50+1)=1326 Ans

Best Regards

[RonPurewal]

this whole problem is WAY WAY WAY beyond the purview of the gmat. in fact, if you're studying this kind of stuff, then i would venture so far as to say that most of the math you're studying is a complete waste of your time, at least as regards the gmat. (i.e., if you're studying this, then you are almost certainly also studying many, many other points of advanced math that would never show up on the test.)

if you're studying books that contain this sort of thing, then you should close those books, and get out books that are designed for the gmat.

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since this problem has no possible connection to the gmat, we probably shouldn't post a solution here. (we don't want forum readers to study irrelevant topics.)