Q: If (1 + x)2n = a0 + a1x + a2x2 + …..+ a2nx2n then
(A) a0 + a2 + a4 + …. = (1/2)( a0 + a1 + a2 + a3 + ….)
(B) an + 1 < an
(C) an–3 = an+3
(D) none of these
Sol. a0 + a1 + a2 + ….= 22n
and a0 + a2 + a4 + ….= 22n–1
an = 2nCn = the greatest coefficient, being the middle coefficient
an–3 = 2nCn–3 = 2nC2n–(n –3) = 2nCn+3 = an+3
Hence (A), (B) and ( C ) are the correct answer.