Asked by Mikey
The coefficient of y^n,y^n+1, y^n+2 in the binomial expansion of (1+y)^14 are in AP. Find the possible values of n.
Answers
Answered by
oobleck
the coefficients are C(14,n+1), C(14,n+2), C(14,n+3)
Due to the symmetry of the coefficients, we only have to consider
n=0,1,2,3,4,5
These sets of coefficients are
1,14,91
14,91,364
91,364,1001
364,1001,2002
1001,2002,3003
2002,3003,3432
So the smallest value of n=4 = 7-3
the other (largest) value would be n+2 = 7+3 = 10, so n=8
Due to the symmetry of the coefficients, we only have to consider
n=0,1,2,3,4,5
These sets of coefficients are
1,14,91
14,91,364
91,364,1001
364,1001,2002
1001,2002,3003
2002,3003,3432
So the smallest value of n=4 = 7-3
the other (largest) value would be n+2 = 7+3 = 10, so n=8
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.