The greatest coefficient in the expansion of $(1+x)²n$ is ________.

Question

If $ A $ and $ B $ are the two real values of $ k $ for which the system of equations $ x + 2y + z = 1 $, $ x + 3y + 4z = k $, $ x + 5y + 10z = k^2 $ is consistent, then $ A + B = $: (a) 3

Answer 1

Step 1: Understanding the Concept
In $(1+x)^N$, the greatest coefficient is the middle one.
Step 2: Evaluation
Here index is $2n$ (even).
Step 3: Middle Term
The middle term coefficient for an even index $N$ is ${}^NC_{N/2}$.
Step 4: Conclusion
Greatest coefficient $= {}^{2n}C_{n}$.
Hence, the Answer is: (A)

The greatest coefficient in the expansion of $(1+x)²n$ is ________.

Show Hint

The Correct Option is A

Solution and Explanation

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