JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of all possible values of \( n \in N \) so that the coefficients of \(x\), \( x^{2} \) and \( x^{3} \) in the expansion of \( (1+x^{2})^{2}(1+x)^{n} \) are in arithmetic progression is :
- A 3
- B 7
- C 12
- D 9
Answer & Solution
Correct Answer
(D) 9
Step-by-step Solution
Detailed explanation
\(\left(x^4+2 x^2+1\right)\left({ }^n C_0 x^0+{ }^n C_1 x^1+{ }^n C_2 x^2+{ }^n C_3 x^3+\ldots\right)\) Coefficient \(x \Rightarrow{ }^{ n } C _1\), coeff. of \(x^2 \Rightarrow 2+{ }^{n} C _2\) \(2+\frac{ n ( n -1)}{2}\) Coeff. of \(x^3=2 \cdot{ }^{n} C_1+{ }^{n} C_3\)…
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