AP EAMCET · Maths · Binomial Theorem
In the expansion of \(\left(a+1+\frac{1}{a}\right)^n\), where \(n \in \mathbf{N}\) there are 2029 terms. Then \(n=\)
- A 1015
- B 1013
- C 1014
- D 1012
Answer & Solution
Correct Answer
(C) 1014
Step-by-step Solution
Detailed explanation
\(\left(a+1+\frac{1}{a}\right)^n=\frac{1}{a^n}\left(a^2+a+1\right)^n\) \(\therefore\) Number of terms \(=2 n+1\) \(\begin{aligned} 2029 & =2 n+1 \\ 2 n & =2028 \\ n & =1014 \end{aligned}\) Hence, option (c) is correct.
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