Question 130

The term independent of x in the expression of $$\left(2x^2 + \frac{1}{x^2}\right)$$ is

we know that general term of expansion (a+b)^n isΒ 

$$Β T_{r+1}$$ = $$nC_{r}$${a}^{n-r}b^nΒ  Β  Β Β Β x$$\geq0$$

Β hereΒ in expressionΒ  $$\left(2x^2 + \frac{1}{x^2}\right)$$Β  we have givenΒ Β  n=1Β  Β  a=2x^2Β  Β Β  b=1\x^2

$$ T_{r+1}$$ =Β $$1C_{r}$${2x^2}^{1-r}{1\x^2}^1

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β =Β  Β $$1C_{r}$${2}^{1-r}{x^2}^{1-r}{1\x^2}^1

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β = Β  Β $$1C_{r}$${2}^{1-r}{x}^{2-2r}{x}^-2r

Β  Β  Β  Β  Β  Β  Β  Β  Β  = Β  Β  $$1C_{r}$${2}^{1-r}{x}^-4r

soΒ  fromΒ  thatΒ Β  n-rΒ =0Β  andΒ  r=4Β  Β  Β  soΒ  Β  Β n=$$5^{th}$$ termΒ  Β  Β Β answerΒ Β  Β  Β  Β 

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