Binomial theorem for positive integral Index

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Question

f the coefficient of the $5^{t h}$ term be the numerically the greatest coefficient in the expansion of $(1 - x)^{n}$ , then the positive integral value of $n$ , is

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Solution

We know that the coefficient of the middle term is
the numerically greatest coefficient in the expansion of $(1 - x)^{n}$
or ${(1 + x)}^{n}$ and its value is $^{n} C_{n / 2}$ or, $\frac{^{n} C_{n + 1}}{2} = \frac{^{n} C_{n - 1}}{2}$ according
as $n$ is even or odd.
It is given that the coefficient of the $5^{t h}$ term is the greatest.
Therefore, $5^{t h}$ term is the middle term. Thus, there are $9$ terms.
Hence $n = 8 .$

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Binomial theorem for positive integral Index

Remember concepts with our Masterclasses.

f the coefficient of the 5th term be the numerically the greatest coefficient in the expansion of (1−x)n, then the positive integral value of n, is

Ready to Test Your Skills?

free study material

f the coefficient of the $5^{t h}$ term be the numerically the greatest coefficient in the expansion of $(1 - x)^{n}$ , then the positive integral value of $n$ , is