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If n=12 m(m in N), prove that ^n C0-(^n...

If `n=12 m(m in N),` prove that `^n C_0-(^n C_2)/((2+sqrt(3))^2)+(^n C_4)/((2+sqrt(3))^4)-(^n C_6)/((2+sqrt(3))^6)+=` ` (-1)^m((2sqrt(2))/(1+sqrt(3)))^ndot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Prove that ^n C1(^n C2)(^n C3)^3(^n Cn)^nlt=((2^n)/(n+1))^(n+1C()2),AA...

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  2. Prove that 1/(m !)^n C0+n/((m+1)!)^n C1+(n(n-1))/((m+2)!)^n C2++(n(n-1...

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  3. If n=12 m(m in N), prove that ^n C0-(^n C2)/((2+sqrt(3))^2)+(^n C4)/(...

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  4. In the expansion of (1 + x)^(n) (1 + y)^(n) (1 + z)^(n) , the sum of t...

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  5. Prove that ^100 C0^(100)C2+^(100)C2^(100)C4+^(100)C4^(100)C6++^(100)C(...

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  6. Prove that sum(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m Cr)=m-1/mdot

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  7. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  8. If b1, b2 bn are the nth roots of unity, then prove that ^n C1dotb1+^n...

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  9. If .^(n+1)C(r+1) :^n Cr :^(n-1)C(r-1)=11 :6:3, then n r=? a. 20 b. 30...

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  10. If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i...

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  11. Find the last two digits of the number (23)^(14)dot

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  12. The value of x for which the sixth term in the expansion of [2^(log)2s...

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  13. If the 6th term in the expansion of(1/(x^(8/3))+x^2(log)(10)x)^8 is 56...

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  14. The total number of terms which are dependent on the value of x in the...

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  15. In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coe...

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  16. If n is an integer between 0 and 21, then the minimum value of n!(21-...

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  17. If R is remainder when 6^(83)+8^(83) is divided by 49, then the value ...

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  18. Let aa n db be the coefficients of x^3 in (1+x+2x^2+3x^3)^4a n d(1+x+2...

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  19. Let 1+sum(r=1)^(10)(3^r.^(10)Cr+r.^(10)Cr)=2^(10)(alpha. 4^5+beta) whe...

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  20. Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C(0)a^(n-1)-""...

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