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

Prove that `(""^nC_r)/(""^nC_(r-1))=(n-r+1)/r`

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Given that C_r/(C_(r-1))=(n-r+1)/r Evaluate C_1/C_0,C_2/C_1 and C_3/C_2

Prove that ""^(n+1)C_(r+1)=(n+1)/(r+1)"^nC_r

Given that ""^nC_r="^nC_(n-r) or C_r=C_(n-r) Prove that aC_0+(a+b)C_1+...+(a+nb)C_n=(2a+nb)2^(n-1) Hence, prove that C_0+5C_1+9C_2+...+(4n+1)C_n=(4n+2)2^(n-1)

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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If tr denotes the r^(th) term in the expansion of (x+1/x)^23 ,find t12...

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

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

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

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

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

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

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  8. Using the (r+1)^(th) term, find the 3rd,4th and 5th terms in the expan...

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  9. find the middle term in the expansion of (3x+2y)^8

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  10. Expand (1+x)^4,(1-x)^3 and (1-x)^2

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  11. Expand (1-x+x^2)^4

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  12. Consider the expansion of ((4x)/5-5/(2x))^9 Find the general term in t...

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  13. Consider the expansion of ((4x)/5-5/(2x))^9 Find the 7th term in the e...

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  14. Consider the expansion of ((4x)/5-5/(4x))^8 Find the (r+1)^(th) term i...

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  15. Consider the expansion of ((4x)/5-5/(4x))^8 Find the number of terms i...

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  16. Consider the expansion of ((4x)/5-5/(4x))^8 The middle term in the exp...

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  17. Consider the expansion of ((4x)/5-5/(4x))^8 Find the fourth term from ...

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  18. Consider the expansion of (3x^3+2/x^2)^40 Find the general term in the...

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  19. Consider the expansion of (3x^3+2/x^2)^40 Assuming the term containing...

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  20. Consider the expansion of (3x^2-1/(2x^3))^10 Find the (r+1)^(th) term ...

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