SOLUTION: If 21st and 22nd term of the expansion (1+x)^44 are equal find the value of x

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Question 1116575: If 21st and 22nd term of the expansion (1+x)^44 are equal find the value of x
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The first term of the expansion is

C%2844%2C0%29%2Ax%5E0+=+1%2A1+=+1

The n-th term of the expansion is

C%2844%2Cn-1%29%2Ax%5E%28n-1%29

So the 21st term is C%2844%2C20%29x%5E20 and the 22nd term is C%2844%2C21%29x%5E21.

We want the two terms to be equal:

C%2844%2C20%29x%5E20+=+C%2844%2C21%29x%5E21

x+=+C%2844%2C20%29%2FC%2844%2C21%29

x+=+%2844%21%2F%28%2820%21%29%2824%21%29%29%29%2F%2844%21%2F%28%2821%21%29%2823%21%29%29%29

x+=+%28%2821%21%29%2823%21%29%29%2F%28%2820%21%29%2824%21%29%29+=+21%2F24+=+7%2F8