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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

JBD PUBLICATION-MODEL PAPER (4)-EXERCISE
  1. Find the principal solutions of cosx=-1/sqrt2.

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  2. Express (-2 - 1/3 i)^3 in the form of a + ib.

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

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  4. Using Binomial Theorem, evaluate each of the following:(99)^5.

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  5. Find the points on x-axis which are at a distance of sqrt29 units from...

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  6. Write the negation of the following statements p: all cats scratch.

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  7. Find the component statements of the following compound statements and...

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  8. Find the range of f(x)=3/(2-x^2).

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  9. Prove that:(1+sin2x-cos2x)/(1+sin2x+cos2x)=tanx

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  10. Find the general solution of the following equations: sin x + sin 3x +...

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  11. Find the general solution of the following equations: cos 3x + cosx- c...

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  12. Using principle of mathematical induction of prove that: 1+2+3+……….+n<...

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  13. Use principle of mathematical induction to prove that:1+2+3+……….+n=(n(...

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  14. Prove the following by using the principle of mathematical induction f...

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  15. Find n if "^(n-1)P3 : "^nP4 =1:9.

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  16. If m times the mth term is equal to n times the nth term of an A.P. pr...

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  17. Without using the pythagorus, show that the points (4, 4), (3, 5) and ...

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  18. Find the equation of a hyperbola whose vertices lie on y-axis, centre ...

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  19. Find the derivative of 2/(x+1)-x^2/(3x-1).

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  20. An integer is chosen from the first 200 integers. Find the probability...

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