Question
Show that the coefficient of the middle term in the expansion of is equal to the sum of the coefficients of two middle terms in the expansion of .
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Solution: Middle terms in expansion are and
So, sum of coefficients of these two middle terms will be,
Now, we will find the coefficient of middle term in expansion .
Coefficient of in
From and , we can see that both values are equal.
So, sum of coefficients of these two middle terms will be,
Now, we will find the coefficient of middle term in expansion .
Coefficient of in
From and , we can see that both values are equal.
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Question Text | Show that the coefficient of the middle term in the expansion of is equal to the sum of the coefficients of two middle terms in the expansion of . |
Answer Type | Text solution:1 |
Upvotes | 150 |