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Prove that C0C2+C1C3+…+C(n-2)Cn=^(2n)C(n...

Prove that `C_0C_2+C_1C_3+…+C_(n-2)C_n=^(2n)C_(n-2)`

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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. Given that C0+C1x+C2x^2+..+Cnx^n=(1+x)^n Prove that C(1).2+C(2).2^2+....

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  2. Find the coefficient of x^4 in the expansion of (1+x)^n(1-x)^n

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  3. Find the coefficient of x^4 in the expansion of (1-x^2)^n

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  4. What is the value of C0+C1+C2+..+Cn?

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  5. What is the value of C0+C2+C4+....?

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  6. What is the value of C1+C3+C5+...?

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  7. Prove that 2C0+C1+2C2+C3+2C4+...=3.2^(n-1)

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  8. What is the coefficient of x^(n-2) in the expansion of (1+x)(1+x)^n?

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  9. What is the coefficient of x^(n-2) in the expansion of (1+x)^(2n)?

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  10. Prove that C0C2+C1C3+…+C(n-2)Cn=^(2n)C(n-2)

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  11. Given that 1/(r+1)""^nCr=1/(n+1)"'^(n+1)C(r+1) Prove that 2""^10C0+2^...

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  12. Find a, b and n in the expansion of (a+b)^n if the first three terms o...

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  13. Find a if the coefficients of x^2 and x^3 in the expansion of (3+ax)^9...

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  14. Find the coefficient of x^5 in the product (1+2x)^6(1-x)^7 using binom...

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  15. If a and b are distinct integers prove that a-b is a factor of a^n-b^n...

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  16. Evaluate (sqrt3+sqrt2)^6-(sqrt3-sqrt2)^6

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  17. Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4

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  18. Find an approximation of (0.99)^5 using the first three terms of its e...

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  19. Expand using Binomial theorem (1+x/2-2/x)^4,xne0

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  20. Find the expansion of (3x^2-2ax+3a^2)^3 using Binomial theorem

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