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If the number of terms in (x + 2+ (1)/(...

If the number of terms in ` (x + 2+ (1)/(x))^(n) (n in I ^(+) " is " 401 `,
then n is greater then

A

201

B

200

C

199

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
d
Now, `(x + 1 + (1)/(x))^(n) = ((1 + x+ x^(2)))/(x^(n))`
Since , ` (1 + x + x^(2))^(n) ` is of the form
` a_(0) + a_(1)x + a_(2)x^(2) + …+ a_(2n) x^(2n)` which contains 2n+ 1 terms .
` therefore 2n + 1 = 401 rArr 2n = 400 rArr n = 200`
which is greater then 199.
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