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If n >2, then prove that C1(a-1)-C2xx(a-...

If `n >2,` then prove that `C_1(a-1)-C_2xx(a-2)++(-1)^(n-1)C_n(a-n)=a ,w h e r eC_r=^n C_rdot`

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MCGROW HILL PUBLICATION-MATHEMATICAL INDUCTION AND BINOMIAL THEOREM-EXERCISE (Numerical Answer Type Questions)
  1. If the coefficient of x^(2) and x^(3) in the expansion of (3+ax)^(11) ...

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  2. If sum(r=0)^(n)(3^(r))(""^(n)C(r))=4096, then n=-

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  3. Coefficient of x^(7) in the expansion of (1+x+x^(2))^(4) is

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  4. The value of (18^3 +7^3+3.187.25)/(3^6+62432+1581.4+2027.8+159.16+ 6....

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  5. If the sixth term in the expansion of [3log(3sqrt(9^(x-1)+7))+1/(3^(...

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  6. In the expansion of (2-3x^3)^(20), if the ratio of 10^(th) term to 11^...

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  7. The expression [x+(x^(3)-1)^((1)/(2))]^(5)+[x-(x^(3)-1)^((1)/(2))]^(...

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  8. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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  9. The sum of the coefficients of the first three terms in the expansion...

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  10. The value of ((""^(50)C(0))/(1)+(""^(50)C(2))/(3)+(""^(50)C(4))/(5)+…....

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  11. If n >2, then prove that C1(a-1)-C2xx(a-2)++(-1)^(n-1)Cn(a-n)=a ,w h e...

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  12. Suppose the sum of the coefficients in the expansion of (1 - 5x + 12x^...

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  13. Let C(r)=""^(15)C(r),(0lerle15), and m=(C(1))/(C(0))+(2C(3))/(C(2))+(3...

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  14. Suppose the coefficient of the middle term in the expansion of (1 + x)...

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  15. If n is an even natural number , then sum(r=0)^(n) (( -1)^(r))/(""^(n)...

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  16. If a > 0 and the coefficient of x^(5) in the expansion of (1+ax)^(2)(1...

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  17. Coefficient of x^(11) in the expaJ}sion of (1 + 3x + 2x^(2))^(6) is

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  18. Find the term independent of x in the expansion of (1+x+2x^3)[(3x^2//2...

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  19. If a:b = 3:5, and sum of the coefficients of 5^(th) and 6^(th) terms i...

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  20. For n = 6, let N=(""^(n)C(0))^(2)+(""^(n)C(1))^(2)+…+(""^(n)C(n))^(2...

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