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The interval in which x (> 0) must lie so that the greatest term in the expansion of (1 + x)2n has the greatest coefficient is
a.
b.
c.
d. None of these?
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Most Upvoted Answer
The interval in which x (> 0) must lie so that the greatest term in th...
Understanding the Problem
In the expansion of (1 + x)^2n, the coefficient of a term represents the number of ways that term can be formed. To find the greatest coefficient, we must find the interval in which x must lie so that the greatest term also has the greatest coefficient.

Analysis of Terms
- The general term in the expansion of (1 + x)^2n is given by C(2n, k) * (1)^(2n-k) * x^k, where k is the power of x.
- The coefficient of this term is C(2n, k), which represents the number of ways this term can be formed.

Finding the Greatest Coefficient
- The greatest coefficient occurs when k is maximum, which is when k = n.
- Therefore, the greatest term in the expansion is C(2n, n) * x^n.

Interval for x
- To ensure that the greatest term also has the greatest coefficient, we need to find the interval for x.
- Since the coefficient C(2n, n) is maximum when x^n is maximum, x must be greater than 0 for x^n to be maximum.
- Therefore, the interval for x (> 0) is the set of all positive real numbers.

Conclusion
- In conclusion, the interval in which x (> 0) must lie so that the greatest term in the expansion of (1 + x)^2n has the greatest coefficient is all positive real numbers.
- By ensuring that x is positive, we guarantee that x^n is maximized, leading to the greatest coefficient in the expansion.
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The interval in which x (> 0) must lie so that the greatest term in the expansion of (1 + x)2n has the greatest coefficient isa. b. c. d. None of these?
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The interval in which x (> 0) must lie so that the greatest term in the expansion of (1 + x)2n has the greatest coefficient isa. b. c. d. None of these? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The interval in which x (> 0) must lie so that the greatest term in the expansion of (1 + x)2n has the greatest coefficient isa. b. c. d. None of these? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The interval in which x (> 0) must lie so that the greatest term in the expansion of (1 + x)2n has the greatest coefficient isa. b. c. d. None of these?.
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