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Question: Answered & Verified by Expert
In the expansion of \(\left(a+1+\frac{1}{a}\right)^n\), where \(n \in \mathbf{N}\) there are 2029 terms. Then \(n=\)
MathematicsBinomial TheoremAP EAMCETAP EAMCET 2020 (18 Sep Shift 2)
Options:
  • A 1015
  • B 1013
  • C 1014
  • D 1012
Solution:
1623 Upvotes Verified Answer
The correct answer is: 1014
\(\left(a+1+\frac{1}{a}\right)^n=\frac{1}{a^n}\left(a^2+a+1\right)^n\)
\(\therefore\) 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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