Combination and induction question

[romo84]

Homework Statement

I need some help with this question please.

Prove using mathematical induction that Σn, j=2 C(j,2) = C(n+1,3) whenever n is an integer greater than 1.

I am not even sure how to get the basis step because it does not makes sense to me to calculate C(j,2), wouldn't that always be C(2,2)?

Thanks for your help.

Homework Equations

The "C" is for "Combination"

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi romo84! welcome to pf!

(try using the X² and X₂ icons just above the Reply box )

I am not even sure how to get the basis step because it does not makes sense to me to calculate C(j,2), wouldn't that always be C(2,2)?

no, it means ∑_j=2ⁿ C(j,2)

 

[romo84]

actually, the n is located above the summation symbol, it is not j=2^n.

any advise?

 

[tiny-tim]

yes i know, but i can't type that!

it means the sum from j = 2 up to j = n

for example, for n = 4, it means (2,2) + (3,2) + (4,2) = (5,3)

 

[romo84]

Thanks very much, I understand what the question is asking now!