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Prove that there is no term containing x...

Prove that there is no term containing `x^(10)` in the expansion of `(x^(2) - 2/x)^(18).`

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The general term in the given expansion is given by
`T _(r+1)= (-1)^(r) xx.^(18)C_(r) xx (x^(2))^((18-r)) xx (2/x)^(r)`
`rArr T_((r+1))=(-1)^(r) xx.^(18)C_(r) xx 2^ (r) xxx^((36-3r))`.
Let `T_(r+1)" contain " x^(10)`. Then,
`36-3r = 10 rArr 3r = 26 rArr r=26/3`
Since the value of r cannot be a fraction , so there is no term containing `x^(10)`.
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RS AGGARWAL-BINOMIAL THEOREM-EXERCISE 10B
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  2. Show that the term independent of x in the expansion of (x-1/x)^(10) ...

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  3. If the coefficents of x^(2) and x^(3) in the expansion of (3+px)^(9)...

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  4. Show that coefficient of x^(-3) in the expansion of (x-1/x)^(11) is -3...

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  5. Show that the middle term in the expansion of ((2x^2)/3+3/(2x)^(2))^(1...

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  6. Show that the coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(...

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  7. Prove that there is no term involving x^(6) is the expansion of (2x^(2...

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  8. Show that the coefficient of x^(4) in the expansion of (1+2x+x^(2))^(5...

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  9. Write the number of terms in the expansion of (sqrt(2)+1)^(5)+ (sqrt(...

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  10. Which term is independent of x in the expansion of (x-1/(3x^(2)))^(9)?

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  11. Write the coefficient of the middle term in the expansion of (1+x)^(2...

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  12. Write the coefficient of x^(7) y^(2) in the expansion of (x+2y)^(9).

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  13. If the coefficent of (r-5)th and (2r-1)th terms in the expansion of (...

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  14. Write the 4th term form the end in the expansion of (3/(x^(2))-x^(3)/6...

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  15. Find the coefficient of x^n in the expansion of (1+x)(1+x)^ndot

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  16. In the binomial expansion of (a+b)^n , coefficients of the fourth and ...

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  17. Find a positive value of m for which the coefficient of x^2 in the ex...

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