First slide

Binomial theorem for positive integral Index

Question

If in the expansion of $(1 + x)^{n}, a, b, c$ are three consecutive coefficients, then n =

Moderate

A

$\frac{ac + ab + bc}{b^{2} + ac}$
B

$\frac{2 ac + ab + bc}{b^{2} - ac}$
C

$\frac{ab + ac}{b^{2} - ac}$
D

none of these

Solution

Here $a =^{n} C_{r}, b =^{n} C_{r + 1} and c =^{n} C_{r + 2}$
Put n = 2, r = 0, then option (b) holds the condition, i.e.,
$n = \frac{2 ac + ab + bc}{b^{2} - ac}$

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