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

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

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PSEB-BINOMIAL THEOREM-EXERCISE
  1. Find (x + 1)^6 + (x -1)^6. Hence or otherwise evaluate (sqrt2+1)^6 + (...

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  2. Show that 9^(n+1) -8n -9 is divisible by 64, whenever n is a positive ...

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

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  4. Find the coefficient of x^5 in (x + 3)^8

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  5. Find the coefficient of a^5 b^7 in (a - 2b)^12 .

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  6. Write the general term in the expansion of (x^2 - y)^6

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  7. Write the general term in the expansion of (x^2 - yx)^12 , x ne 0.

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  8. Find the 4th term in the expansion of (x-2y)^12.

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  9. Find the 13th term in the expansion of (9x-1/(3sqrtx))^18, x ne 0.

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  10. Find the middle terms in the expansion of:- (3- x^3/6)^7

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  11. Find the middle terms in the expansion of:- (x/3+9y)^10.

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  12. In the expansion of (1 + a)^(m+n), prove that coefficients of a^m and ...

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  13. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  14. Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  15. Find a positive value of m for which the coefficient of x^2 in the exp...

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  16. Find a, b and n in the expansion of (a+b)^n if the first three terms o...

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  17. Find a if the coefficients of x^2 and x^3 in the expansion of (3 + ax)...

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  18. Find the coefficient of x^5 in the product (1 + 2x)^6 (1 -x)^7 using b...

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  19. If a and b are distinct integers, prove that a- b is a factor of a^n -...

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  20. Evaluate (sqrt3+sqrt2)^6 - (sqrt3-sqrt2)^6.

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