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in Binomial Theorem by (44.7k points)
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Find the term independent of x in the expansion of : \(\Big(x-\frac{1}{x^2}\Big)^{3n}\)

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Best answer

To Find : term independent of x, i.e. x0 

For \(\Big(x-\frac{1}{x^2}\Big)^{3n}\)

a = x, b = -\(\frac{1}{x^2}\) and N = 3n

We have a formula,

Now, to get coefficient of term independent of x that is coefficient of x0 we must have,

(x)3n-3r = x0 

• 3n - 3r = 0 

• 3r = 3n 

• r = n

Therefore, coefficient of x0 = (n3n)(-1)n

Conclusion : coefficient of x0 =  (n3n)(-1)n

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