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Find the coefficient of x^(50) in the ex...

Find the coefficient of `x^(50)` in the expansion of `(1+x)^(101)xx(1-x+x^2)^(100)dot`

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the coefficient of x^(20) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

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  2. The number of terms in the expansion of (a+b+c)^n where ninN is

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  3. Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x...

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  4. Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

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  5. Find the coefficient of x^k in1+(1+x)+(1+x)^2++(1+x)^n(0lt=klt=n)dot

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  6. The term independent of x in the expansion of (1+x+2x^3)(3/2(x^2)-1/(3...

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  7. If aa n db are distinct integers, prove that a-b is a factor of a^n-b^...

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  8. Find a, b and n in the expansion of (a+b)^(n) if the first three term...

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  9. Find the coefficient of x^(25) in expansion of expression sum(r=0)^(50...

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  10. If the sum of the coefficients of the first, second, and third terms ...

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  11. If p+q=1, then show that sum(r=0)^nr^2^nCrp^rq^(n-r)=npq+n^2p^2

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  12. If every pair from among the equations x^2+a x+b c=0. x^2+b x+c a=0,a ...

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  13. Prove that ^mC1^n Cm-^m C2^(2n)Cm+^m C3^(3n)Cm-.....=(-1)^(m-1)n^mdot

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  14. Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn +^nC2 ^(2n-4)Cn =2^n

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  15. Find the sum sum(r=0) .^(n+r)Cr .

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  16. Find the value of (sumsum)(0leiltjlen) (i+j)(""^(n)C(i)+""^(n)C(j)).

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  17. Find the sum sumsum(0lt=i<jlt=n-1)^n Cidot

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  18. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

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  19. Find the sum (sumsum)(0leiltjlen) ""^(n)C(i).""^(n)C(j).

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  20. Prove that sum(r=0)^ssum(s=1)^n^n Cs^s Cr=3^n-1.

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