Question

Which term in the expansion of (x-1/x)^7 is independent of x.
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No Faltu answers. Class 11th Binomial Expansion.
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HINT - What I want here is a constant, ie. Cx⁰ where C = Const

Answer 1

Answer: No any is  independent of x

Step-by-step explanation:  

Let (r+1)th term be independent  of  x  in the given expression.

Now,

$T_{r+1}={^7}C_r.(x)^{7-r}.(-\frac{1}{x})^r\\\;\\={^7}C_r.(x)^{7-r}.(-1)^r.(\frac{1}{x})^r\\\;\\={^7}C_r.(x)^{7-r}.(-1)^r.(x)^{-r}\\\;\\={^7}C_r.(x)^{7-r-r}.(-1)^r\\\;\\={^7}C_r.(x)^{7-2r}.(-1)^r$

This  term will be independent  of  x, iff

7-2r = 0

r = 7/2

We get  a fractional value  of r. We know  that  number of  terms  can not  be  fractional. Hence this  value of  r is  invalid.

We can conclude that  there in no  any  term independent  of  x in expansion of (x-1/x)^7