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 :/ )

viola Jul 15, 2021

#1**+2 **

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

https://web2.0calc.com/questions/binomial-theorem-question-pls-help

CPhill Jul 15, 2021

#2**+2 **

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 $\binom{n}{k}$

MathProblemSolver101 Jul 15, 2021