Asked by Anonymous
Find the numerical value of the coefficient x^11 in the expansion of (x^2+1/x)^10 in the powers of x.
Answers
Answered by
Reiny
general term = term(r+1)
=C(10,r) (x^2)^(10-r) (1/x)^r
= C(10,r) x^(20 - 2r) x^(-r)
= C(10,r) x^(20 -3r)
so 20 -3r = 11
-3r = -9
r = 3
C(10,3) = 120
the term containing x^11 is 120x^11 and it is the 4th term
confirmation by Wolfram:
http://www.wolframalpha.com/input/?i=expand+%28x%5E2%2B1%2Fx%29%5E10
=C(10,r) (x^2)^(10-r) (1/x)^r
= C(10,r) x^(20 - 2r) x^(-r)
= C(10,r) x^(20 -3r)
so 20 -3r = 11
-3r = -9
r = 3
C(10,3) = 120
the term containing x^11 is 120x^11 and it is the 4th term
confirmation by Wolfram:
http://www.wolframalpha.com/input/?i=expand+%28x%5E2%2B1%2Fx%29%5E10
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.