In the binomial expansion of (a-b)n, n≥5, the sum of the 5thand 6th terms is 0. Then ab=?
(n–5)6
(n–4)5
5(n–4)
6(n–5)
Explanation For The Correct Option:
Finding abin the given binomial expansion:
(r+1)thterm in the expansion of (a-b)n
Tr+1=nCran-rbr....(i)
Given that T5=0&T6=0
⇒T5+T6=0⇒T4+1+T5+1=0⇒nC4an-4-b4-nC5an-5-b5=0[fromequation(i)]⇒nC4an-4-b4=nC5an-5-b5⇒n!4!(n-4)!ana4b4=n!5!(n-5)!ana5b5⇒14!(n-4)(n-5)!=15×4!(n-5)!ba⇒1(n-4)=15ba⇒ab=(n-4)5
Hence, the correct answer is option (B).