Q.
if a1,a2,a3a,4 are the coefficients of any four consecutive terms in the expansion of (1+x)n, then a1a1+a2+a3a3+a4 is equal to
see full answer
Want to Fund your own JEE / NEET / Foundation preparation ??
Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*
An Intiative by Sri Chaitanya
a
a2a2+a3
b
12a2a2+a3
c
2a2a2+a3
d
2a3a2+a3
answer is C.
(Unlock A.I Detailed Solution for FREE)
Ready to Test Your Skills?
Check your Performance Today with our Free Mock Test used by Toppers!
Take Free Test
Detailed Solution
Let a1,a2, a3, a4 be respectively the coefficients of(r + 1)th, (r + 21)th, (r + 3)th and (r + 4)th terms in theexpansion of (1 + ,x)n .Then,a1=nCr, a2=nCr+1, a3=nCr+2, a4=′Cr+3Now a1a1+a2+a3a3+a4= nCr nCr+nCr+1+ nCr+2 nCr+2+nCr+3 = nCr n+1Cr+1+ nCr+2n+1Cr+3 ∵nCr+nCr+1=n+1Cr+1= nCrn+1r+1nCr+ nCr+2n+1r+3nCr+2 ∵nCr=nrn−1Cr−1=r+1n+1+r+3n+1=2(r+2)n+1=2 nCr+1 n+1Cr+2=2 nCr+1 nCr+1+nCr+2=2a2a2+a3
Watch 3-min video & get full concept clarity