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If |x| lt 1, then the coefficient of x^(...

If `|x| lt 1`, then the coefficient of `x^(n)` in expansion of `(1+x+x^(2)+x^(3)+"…..")^(2)` is

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
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  2. Let R=(5 sqrt 5+11)^(2n+1) and f=R-[R] where [] is the greatest intege...

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  3. If |x| lt 1, then the coefficient of x^(n) in expansion of (1+x+x^(2)+...

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  4. The coefficient of x^5in(1+2x+3x^2+)^(-3//2)i s(|x|<1)

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  5. If x is so small that x^3 and higher powers of x may be neglected, the...

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  6. If x is positive, the first negative term in the expansion of (1+x)^(2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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