There are two parts to this question.


(a) Simplify  n choose k / n choose k-1.
This is easy for me. I can expand n choose k and n choose k-1 and simplify to get (n-k+1)/k.

(b) For some positive integer n the expansion of (1+x)^n has three consecutive coefficients  a,b,c  that satisfy a:b:c 1:7:35  (ratio). What must n be?
This the part I need help with, i find this part confusing.

(sorry if my formatting is bad :/ )

 Jul 15, 2021

For  the second one......here's a similar problem solved  by heureka.....see if it might help.....






cool cool cool

 Jul 15, 2021

Hint: Evaluate each of $\binom{n}{k-1}, \binom{n}{k}, \binom{n}{k+1}$ (which can be found in heureka's answer if you're stuck.)


Hint 2: You know $\frac{\binom{n}{k}}{\binom{n}{k-1}} = \frac{n - k + 1}{k},$ you have $\binom{n}{k} = \binom{n}{k-1} \left(\frac{n - k + 1}{k}\right)$ and $\binom{n}{k-1} = \frac{k \binom{n}{k}}{n-k + 1}$. Evaluate $\binom{n}{k+1}$ in terms of $\binom{n}{k}$

 Jul 15, 2021
edited by MathProblemSolver101  Jul 15, 2021

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