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Prove that the coefficient of x^n in th...

Prove that the coefficient of `x^n` in the expansion of `(1+x)^(2n)` is twice the coefficient of `x^n` in the expansion of `(1+x)^(2n-1)`

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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. In the expansion of (1+a)^(m+n), prove that the coefficient of a^m and...

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  2. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  3. Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is ...

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  4. Find the positive value of m for which the coefficient of x^2 in the e...

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  5. Consider the expansion of (3x-x^3/6)^8 Find the general term in the ex...

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  6. Consider the expansion of (3x-x^3/6)^8 How many terms are there in the...

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  7. Consider the expansion of (3x-x^3/6)^8 Find the middle term in the exp...

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  8. Find the coefficient of middle term in the expansion of (1+a)^8

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  9. Find the coefficient of the middle term in the expansion of (1+a)^7

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  10. Consider (sqrt2+3^(1//5))^10 Find the r+1^(th) terms in the expansion ...

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  11. Consider (sqrt2+3^(1//5))^10 If the r+1^(th) term is rational , find r...

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  12. Write the first three terms in the expansion of (1+ax)^n,ninN

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  13. If the first three terms in the expansion of (1+ax)^n are 1,6x and 16x...

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  14. If tr denotes the r^(th) term in the expansion of (x+1/x)^23 ,find t12...

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  15. Let cr denote the binomial coefficient "^nCr Write the factorial formu...

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  16. Prove that (""^nCr)/(""^nC(r-1))=(n-r+1)/r

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  17. Let cr denote the binomial coefficient "^nCr Hence, show that C1/C0+2C...

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  18. Given that ""^nCr="^nC(n-r)or Cr=C(n-r) Prove that aC0+(a+b)C1+...+(a+...

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  19. Given that ""^nCr="^nC(n-r)or Cr=C(n-r) Prove that aC0+(a+b)C1+...+(a+...

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  20. What is the (r+1)^(th) term in the expansion of (3x+2y)^8?

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