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Show that the middle term in the expansi...

Show that the middle term in the expansion of `(1+x)^(2n)i s((1. 3. 5 (2n-1)))/(n !)2^n x^n ,w h e r en` is a positive integer.

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MAHAVEER PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. Find the coefficient of x^(-8) in the expansion of (x-1/(2x^2))^10

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  2. Find a if 17th and 18th terms in the expansion of (2+a)^(50) are eq...

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

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  4. Find the term independent of x in (2x^2-1/x)^12. Also write its 3^(rd)...

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  5. Evaluate : (1+sqrt7)^5+(1-sqrt7)^5

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  6. Find the middle term in the expansion of : \ (x-1/x)^(10)

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  7. Find the coefficient of a^15 in the expansion of (a^3+2/a^2)^10

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  8. If (1+x)^n=C0+C1x+C2x^2+ +Cnx^n, Prove that, C1+2C2+3C3++nCn=n.2^(n-1)...

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  9. Find the co-efficient of x^17 in (x-x^2)^10.

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  10. Find the co-efficient of 1/x in the expansion of (3/x^2-x^3/3)^8.

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  11. Expand of the expression : (2x-3)^6

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  12. Expand of the expression : (x/3+1/x)^5

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  13. Expand of the expression : (x+1/x)^6

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  14. Find (a+b)^4-(a-b)^4. Hence, evaluate (sqrt3+sqrt2)^4-(sqrt3-sqrt2)^4.

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  15. Find a if the 7th and 18th terms of the expansion (2+a)^(50) are equal...

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  16. Find the coefficient of x^6y^3 in the expansion of (x+2y)^9dot

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  17. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  18. Find middle term of (x+2/(x^2))^17

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  19. Find middle term of (x+2/(x^2))^16

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  20. Find the middle term in the expansion of (3x-(x^3)/6)^9

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