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Prove that .^n C0 . ^(2n) Cn- ^n C1 . ...

Prove that ` .^n C_0 . ^(2n) C_n- ^n C_1 . ^(2n-2)C_n+^n C_2 . ^(2n-4)C_n-=2^ndot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
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  2. Find the fourth term in the expansion of (1-2x)^(3//2)""dot

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  3. Prove that .^n C0 . ^(2n) Cn- ^n C1 . ^(2n-2)Cn+^n C2 . ^(2n-4)Cn-=2...

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  4. Prove that ^n C0 .^n C0-^(n+1)C1 . ^n C1+^(n+2)C2 . ^n C2-=(-1)^ndot

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  5. Find the sum of the coefficients of all the integral powers of x in th...

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  6. If the sum of the coefficient in the expansion of (alpha^2x^2-2alphax+...

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  7. Prove that sum(alpha+beta+gamma = 10) (10 !)/(alpha!beta!gamma!)=3^(10...

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  8. If (1+x-2x^2)^(20)=a0+a1x+a2x^2+a3x^3+...+a(40)x^(40), then find the v...

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  9. Find the sum of the series .^15 C0+^(15)C1+^(15)C2+...............+^(1...

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  10. Find the sum sum(k=0)^(10).^(20)Ck.

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  11. Find the sum of all the coefficients in the binomial expansion of (x^2...

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  12. If the sum of coefficient of first half terms in the expansion of (x+y...

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  13. Find the value of sum(p=1)^n(sum(m=p)^n.^nCm.^m Cp)dot And hence, find...

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

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  15. If the middle term in the expansion of (x^2+1//x)^n is 924 x^6 , then...

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  16. The first three terms in the expansion of (1+a x)^n(n!=0) are 1,6xa n ...

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  17. If x^4 occurs in the rth term in the expansion of (x^4+1/(x^3))^(15), ...

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  18. Find the coefficient of x^(-10) in the expansion of (a/x+b x)^(12) .

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  19. Find the constant term in the expansion of (x-1//x)^6dot

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  20. If the coefficients of (r-5)t h a n d(2r-1)t h terms in the expansion ...

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