Understanding Binomial Coefficients: Finding the r-th term formula

AI Thread Summary
The discussion focuses on understanding binomial coefficients and the formula for the r-th term in a binomial expansion. The general term is given as T_n+1 = C_n^r a^{n-r} b^r, and the user seeks clarification on the r-th term formula and the variables a and b. They have constructed a Pascal triangle up to the 10th row to aid their understanding. The user also references the binomial expansion formula (a+b)^{n} = ∑_{k=0}^{n} C_{n}^{k} a^{n-k} b^{k} as a basis for their inquiry. The conversation invites further assistance on the (n-1) term aspect of the problem.
gschjetne
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I'm working on an IB mathematics portfolio, and here's a problem I don't understand:
The formula for the general term is
<br /> T_n+1=C_n^r a^{n-r} b^r<br />
Verify this formula by examples. This is the formula for the (r+1)-th term.
What would the formula for the r-th term be?
It's not specified what a and b is supposed to represent. That's where I need some explanation.
I already made a nice Pascal triangle all the way to the 10th row.
All help is appreciated.
 
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My guess is that it comes from the expansion:

(a+b)^{n}=\sum_{k=0}^{n}C_{n}^{k} a^{n-k}b^{k}

Daniel.

PS.Can u handle the (n-1) term part??
 
Thanks, I'll give it a try
 

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