Question

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binomial theorem: (3x-5)^4n-3 has 26 terms find the value of n

Answer 1

i believe it should be
4n-3=26-1
n=7

because if you notice, a binomial expands out to one more term that its power

Answer 2

@Auxuris hmm so why would you do 26-1? Is it because of the fact that \[T _{r+1}\]
so it would be 4n-3=25?
25-3 = 22
22/4 = 5.5?...
You plug in or no? Could you show a step by step sequence? :0 With the formulas and all?

Answer 3

you mean 25+3...

Answer 4

oh sure okay
yes i used the general term method and got this
4n-3=26-1
4n=26-1+3
4n=28
n=7

when you plug it back in,
(3x-5)^4n-3
= (3x-5)^4(7)-3
= (3x-5)^25

and if you expand it, you'll get 26 terms

Answer 5

...oh..
sooo it would be 28/4 = 7 ahh gotcha on that part! Ahh gosh thanks so much!

Answer 6

haha no prob ^^

Answer 7

@Auxuris however, can I ask you another question, i'll give you another medal :D

I'm struggling on how to answer this:

Find c given that the expansion (1+cx)(1+x)^4 includes the term 22x^3
I know you need 4 choosing 3 something, with nCr on the calculator, how would I actually do this?

Answer 8

you can't give two medals xD but it's okay, i don't come here for medals

excellent, you're giving me practice on something i need
so you need to compare coefficients

say look at the right side, (1+x)^4
you're right, its a 4C3, which when expanded looks like


4x^3 will then be paired with the 1 in (1+x) in order to get something with x^3
follow? (:

it would be, (4x^3)(1)=4x^3