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  • If the expansion of (x-1/x^2 )^2n contains a term independent of x, then n is a multiple of 2.

If the expansion of  (x-1/x2)2n  contains a term independent of x, then n is a multiple of 2.

 

Answers (1)

The given statement is False.

Given: \left ( x-\frac{1}{x^{2}} \right )^{2n}

Now,

Tr+1 = 2nCr(x)2n-r (-1/x2)r

          = 2nCr(x)2n-r-2r(-1)r

          = 2nCr(x)2n-3r (-1)r(-1)r

Now, for the independent term of x,

2n – 3r = 0

Thus, r = 2n/3, viz. not an integer

Thus, this expression is not possible to be true.

Posted by

infoexpert22

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