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value of the series a(0)-a(2) + a(4)-a(...

value of the series ` a_(0)-a_(2) + a_(4)-a_(6) +…..` is

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If (1 + x + x^(2))^(48) = a_(0) + a_(1) x + a_(2) x^(2) + ... + a_(96) x^(96) , then value of a_(0) - a_(2) + a_(4) - a_(6) + … + a_(96) is

If (1+2x^(2))^(6)=1+a_(1)=a_(2)x^(2)a_(3)x^(3)+...+a_(12)x^(12) then the value of expression a_(2)+a_(4)+a_(6)+...+a_(12) is 322.313.634.64

If (1 + x + x^(2) + x^(3))^(n)= a_(0) + a_(1)x + a_(2)x^(2) + a_(3) x^(3) +...+ a_(3n) x^(3n) , then the value of a_(0) + a_(4) +a_(8) + a_(12)+….. is

If (1 + x)^(2n) = a_(0) + a_(1) x + a_(2) x^(2) +… + a_(2n) x^(2n) , then (a_(0) - a_(2) + a_(4) - a_(6) +…- a_(2n))^(2)+(a_(1) - a_(3) + a_(5) - a_(7) +...+a_(2n-1))^(2) is equal to

(1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2) +......+a_(n)x^(n) then Find the sum of the series a_(0) +a_(2)+a_(4) +……

If (1 + x+ 2x^(2))^(20) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(40) x^(40) . The value of a_(0) + a_(2) + a_(4) + …+ a_(38) is

If a_(0), a_(1), a(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .

Given that (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+......+a_(2n)x^(2n) , find the values of a_(0)-a_(1)+a_(2)-a_(3)......+a_(2n) ,

Let a_(1)=0 and a_(1),a_(2),a_(3),...,a_(n) be real numbers such that |a_(i)|=|a_(i-1)+1| for all i then the A.M.of the numbers a_(1),a_(2),a_(3),...,a_(n) has the value A where

If a_(1)+a_(2)+a_(3)+a_(4)+a_(5)...+a_(n) for all a_(i)>0,i=1,2,3dots n. Then the maximum value of a_(1)^(2)a_(2)a_(3)a_(4)a_(5)..a_(n) is

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. Resolve into the linear factor: a^3+b^3

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  2. Resolve into the linear factor: a^3+b^3+c^3-3abc

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  3. value of the series a(0)-a(2) + a(4)-a(6) +….. is

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  4. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a1-a3+a5-a7+… .

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  5. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a0+a3+a6+a9+… .

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  6. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

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  7. If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : (1...

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  8. If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : 1+...

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  9. If alpha is an n^(th) roots of unity, then 1+2alpha+3alpha^(2)+……..+n...

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  10. If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + ...

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  11. sum(p=1)^pi(3p+2)[sum(q=1)^10sin(2qpi)/11-icos(2qpi)/11]^p

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  12. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

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  13. If alpha ia ROOT OF x^2+x+1= 0 then show that alpha is also a root of...

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  14. If p,q,r are three consecutive integers ge3, prove that x^p+x^q+x^r is...

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  15. If n is n odd integer that is greater than or equal to 3 but not la ul...

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  16. If z^2(bar omega)^4=1 where omega is a nonreal complex cube root of 1 ...

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  17. Find z satisfying |z-5i|le3 such that amp z is the minimum.

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  18. If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals

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  19. Find the complex number Z, the greatest in absolute value which satisf...

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  20. Complex number z1, z2 and z3 in AP

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