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Prove that Sigma(r=1) ""^(n)C(r).3^(r)=4...

Prove that `Sigma_(r=1) ""^(n)C_(r).3^(r)=4^(n)`

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

Prove that Sigma_(r=0)^(n) 3^(r)""^(n)C_(r)=4^(n)

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) .

If x + y = 1 , prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r) = nx .

If ((n),(r )) "denotes " ""^nC_r then (a) Evalutae : 2^(15)((30),(0))((30),(1))-2^(14)((30),(1))((29),(14))+2^(13)((30),(2))((28),(13)).......-((30),(15))((15),(0)) ( b) Prove that : Sigma_(r=1)^(n) ((n-1),(n-r))((n),(r))=((2n-1),(n-1)) ( c) Prove that : ((n),(r))((r),(k))=((n),(k))((n-r),(r-k))

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

Prove that sum_(r=0)^(2n) r.(""^(2n)C_(r))^(2)= 2.""^(4n-1)C_(2n-1) .

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

Prove that : (""^(n)C_(r+1))/(""^(n)C_(r))=(n-r)/(r+1)

Prove that sum_(r=1)^(k) (-3)^(r-1) ""^(3n)C_(2r-1) = 0 , where k = 3n//2 and n is an even integer.

NAGEEN PRAKASHAN ENGLISH-BINOMIAL THEOREM-Exercise 8A
  1. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

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  2. If x= sqrt5+sqrt3 and y = sqrt5-sqrt3, then x^4 -y^4

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  3. Find the values of the following using binomial theorem: (i) 49^(4)...

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  4. By using binomial theorem find which number is greater (1.2)^(3000) " ...

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  5. Prove that Sigma(r=0)^(n) ""^(n)C(r).3^(r)=4^(n)

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  6. If n is a positive integer then find the number of terms in the expans...

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  7. Find the number of terms in the expansion of (1+3x+3x^(2)+x^(3))^(15)

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  8. If (1+x+x^(2))^(n)=1 +a(1)x+a(2)x^(2)+a(3)x^(3) +……..+a(2n).x^(2...

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  9. Using binomial theorem, prove that 2^(3n)-7n-1 is divisible by 49 , wh...

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  10. Expand using binomial theorem: (i) (1-2x)^(4)

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  11. Evaluate using binomial theorem: (i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6...

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  12. Using binomial theorem, expand {(x+y)^5+(x-y)^5}dot and hence find the...

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  13. Expand (x+y)^(4)-(x-y)^(4). Hence find the value of (3+sqrt(5))^(4) -(...

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  14. Find the values of the following using binomial theorem: (i) 49^(4)...

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  15. By using binomial theorem find which number is greater (1.2)^(3000) " ...

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  16. Prove that Sigma(r=1) ""^(n)C(r).3^(r)=4^(n)

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  17. If n is a positive integer then find the number of terms in the expans...

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  18. Find the number of terms in the expansion of (1+3x+3x^(2)+x^(3))^(15)

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  19. If (1-x+x^2)^n=a0+a1x+a2x^2+ .........+a(2n)x^(2n),\ find the value o...

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  20. By using binomial theorem prove that (2^(3n)-7n-1) is divisible by ...

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