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Prove that Sigma(r=))^(n) ""^(n)C(r).3^...

Prove that `Sigma_(r=))^(n) ""^(n)C_(r).3^(r)=4^(n)`

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In a DeltaABC , prove that Sigma_(r=0)^(n)""^(n)C_(r)a^(r)b^(n-r) cos ( r B-(n-r)A)=c^(n) .

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

Prove that sum_(r=0)^(n)3^(rn)C_(r)=4^(n)

"^(n)C_(r)=^(n)C_(n-r)

Prove that sum_(r=0)^(2n)(.^(2n)C_(r))^(2)=n^(4n)C_(2n)

Prove that sum_(r=0)^(n)r(n-r)C_(r)^(2)=n^(2)(^(2n-2)C_(n))

prove that sum_(r=0)^(n)3^(r)nC_(r)=4^(n)

Prove that ""^(n)P_(r )= ""^(n)C_(r )*^rP_(r ) .

NAGEEN PRAKASHAN-BINOMIAL THEOREM-Example
  1. Prove that Sigma(r=))^(n) ""^(n)C(r).3^(r)=4^(n)

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  2. Using binomial theorem, write down the expansions of the following: (2...

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  3. Expand (3x-2y)^(6) with the help ob binomial theorm.

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  4. Simplify with the help of binomial theorm.

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  5. (iii) Find an approximate value of (0.99)^5 using the first three term...

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  6. Using binomial theorem, prove that (101)^(50)> 100^(50)+99^(50)dot

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  7. If number of terms in the expansion of (x -2y +3z)^n are 45, then n i...

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  8. Prove that overset(n)underset(r=0)(Sigma^(n))C(r).4^(r)=5^(n)

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  9. If (1-x+x^(2))^(4)=1+P(1)x+P(2)x^(2)+P(3)x^(3)+...+P(8)x^(8), then pro...

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  10. If o be the sum of odd terms and E that of even terms in the expansion...

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  11. Find the 8th term in the expansion of ((2x)/(3)-(3)/(5x))^(12)

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  12. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  13. Find the 15th term in the expansion of "("sqrt(x)-sqrt(y)")"^(17)

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  14. Find the middle term in the expansion of (3x-(1)/(2x))^(16)

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  15. Find the middle term in the expansion of (1+2x+x^(2))^(10)

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  16. Find the 4th term from the end in the expansion of (1-3x)^(10)

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  17. Show that the middle term in the expansion of (1+x)^(2n)i s((1. 3. 5 (...

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  18. how that the coefficient of (r+1) th in the expansion of (1+x)^(n+1) ...

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  19. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

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  20. Find the coefficient of x^(6) in the expansion of (2x^(3)-(1)/(3x^(3))...

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  21. Find the coefficient of x^(7) in the expansion of (2x^(2)-(1)/(x))^(2...

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