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Prove that: sum(r=0)^(n) 3^( r) ""^(n)C(...

Prove that: `sum_(r=0)^(n) 3^( r) ""^(n)C_(r) = 4^(n)`.

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Prove that sum_(r=0)^n 3^r "^nC_r= 4^n .

Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

The vaule of sum_(r=0)^(n-1) (""^(C_(r))/(""^(n)C_(r) + ""^(n)C_(r +1))) is equal to

Prove that "^nC_r+2 ^(n)C_(r-1)+ ^(n)C_(r-2) = ^(n+2)C_r .

If a + b = k, when a, b gt o and S(k, n) = sum _(r=0)^(n) r^(2) (""^(n) C_(r) ) a^(r) cdot b^(n-r) , then

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

Prove that underset (r=0) overset (n) sum 3^r ""^nC_r =4^n .

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

sum_(r=1)^(n) {sum_(r1=0)^(r-1) ""^(n)C_(r) ""^(r)C_(r_(1)) 2^(r1)} is equal to

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Subjective Type Questions)
  1. If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 ...

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  2. The set of values of a for which the equation Sin^4 x + Cos^4 x = a ha...

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  3. If aa n db are positive quantities such that a > b , the minimum value...

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  4. If alpha+beta+gamma=2pi, then show that tan.alpha/2 + tan.beta/2 + tan...

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  5. Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...

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  6. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...

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  7. Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...

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  8. lf cos^2 alpha -sin^2 alpha = tan^2 beta, then show that tan^2 alpha...

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  9. If A, B, C are the angle of a triangle and |(sinA,sinB,sinC),(cosA,...

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  10. In any DeltaABC, prove that Sigma (sqrt(sinA))/(sqrt(sinB)+sqrt(sinC...

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  11. Find all value of theta which satisfy, sin ( 3 theta + alpha ) + si...

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  12. If the quadratic equation , 4^(sec^(2)alpha) x^(2) + 2x + (beta^(2)-...

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  13. If 2costheta=x+1/x, prove that 2cos3theta=x^3+1/x^3

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  14. If (cos theta(1))/(cos theta(2))+(sin theta(1))/(sin theta(2))=(cos th...

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  15. Prove that sum(k=1)^(n-1) ""^(n)C(k)[cos k x. cos (n+k)x+sin(n-k)x.s...

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  16. Solve sin 2x gt sqrt(2) sin^(2) x+ (2-sqrt(2))cos^(2)x

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  17. The number of solutions of the equation cos[x]=e^(2x-1), x in [0, 2pi]...

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  18. Prove that: sum(r=0)^(n) 3^( r) ""^(n)C(r) = 4^(n).

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  19. Resolve Z^5+ 1 into linear & quadratic factors with real coefficients...

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  20. Prove that the roots of the equation 8x^(3)-4x^(2)-4x+1=0 " are " co...

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