homeschool girl
Junior Member
- Joined
- Feb 6, 2020
- Messages
- 123
For some positive integer [MATH]n,[/MATH] the expansion of [MATH](1 + x)^n[/MATH] has three consecutive coefficients [MATH]a,[/MATH] [MATH]b,[/MATH] [MATH]c[/MATH] that satisfy [MATH]a:b:c = 1:7:35.[/MATH] What must [MATH]n[/MATH] be?
I think i need to solve it by using the binomial theorem like this:
[MATH]7\cdot\binom{n}{r}\cdot1^{n-r}\cdot x^r=\binom{n}{r+1}\cdot1^{n-(r+1)}\cdot x^{r+1}[/MATH]
[MATH]35\cdot\binom{n}{r}\cdot1^{n-r}\cdot x^r=\binom{n}{r+2}\cdot1^{n-(r+2)}\cdot x^{r+2}[/MATH]
but I'm not sure. can someone please help?
I think i need to solve it by using the binomial theorem like this:
[MATH]7\cdot\binom{n}{r}\cdot1^{n-r}\cdot x^r=\binom{n}{r+1}\cdot1^{n-(r+1)}\cdot x^{r+1}[/MATH]
[MATH]35\cdot\binom{n}{r}\cdot1^{n-r}\cdot x^r=\binom{n}{r+2}\cdot1^{n-(r+2)}\cdot x^{r+2}[/MATH]
but I'm not sure. can someone please help?