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If the expansion in powers of x of the f...

If the expansion in powers of `x` of the function `1/[(1-a x)(1-b x)]` is a`a_0+a_1x+a_2x^2+a_3x^3+ ,t h e na_n i s` a.`(b^n-a^n)/(b-a)` b. `(a^n-b^n)/(b-a)` c. `(b^(n+1)-a^(n+1))/(b-a)` d. `(a^(n+1)-b^(n+1))/(b-a)`

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If x is positive, the first negative term in the expansion of (1+x)^(2...

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  2. Value of sum(k=1)^oosum(r=0)^k1/(3^k)(k Cr) is 2/3 b. 4/3 c. 2 d. 1

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  3. If the expansion in powers of x of the function 1/[(1-a x)(1-b x)] is ...

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  4. If f(x)=1-x+x^2-x^3+. . -x^(15)+x^(16)-x^(17) , then the coefficient o...

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  5. The sum of rational in (sqrt2+root(3)(3)+root(6)(5))^10 is equal to

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  6. The value of underset(r=0)overset(10)sum(r).^(20)C(r) is equal to

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  7. If P = (8 + 3sqrt(7))^(n) and f = p - [p] , where [*] denotes the grea...

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  8. Find the GP whose first term is 64 and next term is 32.

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  9. The fifth term of GP is 81 and second term is 24. Find the GP

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  10. The value of x for which the sixth term in the expansion of [2^(log(...

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  11. Find the 7th term of the GP, sqrt(3)+1, 1 , (sqrt(3) -1)/2 ,.....

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  12. The number 51^(49)+51^(48)+51^(47)+........+51+1 is divisible by a. 10...

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  13. If sum(r=0)^(n) (r)/(""^(n)C(r))= sum(r=0)^(n) (n^(2)-3n+3)/(2.""^(n)C...

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  14. If (1+x)^n=C0+C1x+C2x^2+.......+Cn x^n , then show that the sum of the...

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  15. If sum(r=0)^(n){a(r)(x-alpha+2)^(r)-b(r)(alpha-x-1)^(r)}=0, then

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  16. Let a=(2^(1//401)-1) and for each ngeq2,l e tbn=^n C1+^n C2dota+^n C3...

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  17. Prove that underset(r=0)overset(n)sum.^(n)C(r)(-1)^(r)[i^(r)+i^(2r)+i^...

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  18. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

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  19. If the first and third term is 2 and 8 respectively. Find its secon...

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  20. Find the next two terms of the series 2,-6,18,-54,.....

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