How to Verify the 5th Term of the Binomial Expansion of (3-2/x)^9?

  • Thread starter Thread starter donniemateno
  • Start date Start date
  • Tags Tags
    Binomial Series
AI Thread Summary
To verify the 5th term of the binomial expansion of (3-2/x)^9, the general term formula is applied: T(r+1) = n!/(n-r)!r! * A^(n-r) * B^r. For this case, r is set to 4, A is 3, B is -2/x, and n is 9. The calculated term results in -489888/x^4. To check the answer, one should ensure the correct application of the formula and confirm the sign of each component in the expansion.
donniemateno
Messages
44
Reaction score
0
hi there I am abit stuck here. i got a q saying :
in binomial expansion of (3-2/x)^9 find the 5th term using the general term of the binomial expansion and check your answer

(3-2/x)^9

used formula

=N!/(n-r)!r! * A^(n-r) * b ^ r

r= 4
a= 3
b= - 2/x
n=9

got a answer of -489888/x^4

How do i go about checking my answer??
 
Physics news on Phys.org
My answer is like yours, but without the negative sign.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Find the ##r^{th}## term of ##(a+2x)^n##
Replies
3
Views
2K
Binomial Theorem - determine the term with...
Replies
18
Views
2K
Where Did ##(n−r+1)^{th}## Come From in Binomial Expansion?
Replies
3
Views
1K
What are the constants in the binomial series expansion for (1+mx)^-n?
Replies
34
Views
4K
Need help understanding the binomial series
Replies
3
Views
2K
Use of binomial theorem in a sum of binomial coefficients?
Replies
1
Views
2K
Binomial expansion of term with x^2
Replies
4
Views
3K
Express ##x^3+y^3## in terms of ##m## and ##n##
Replies
17
Views
3K
Solve Binomial Theorem Homework: Find Coefficients of Degree 17 & x7
Replies
15
Views
2K
Efficiently Calculate Binomial Expansion Coefficients | Homework Equations
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top