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

If p+q=1, then show that `sum_(r=0)^nr^2^nC_rp^rq^(n-r)=npq+n^2p^2`

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the coefficient of x^(25) in expansion of expression sum(r=0)^(50...

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

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

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

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

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

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

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

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

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

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

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  13. Find the sum sumsum(0leiltjlen)"^nCi

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  14. Find the coefficient of x^4 in the expansion of (x/2-3/x^2)^10.

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  15. Find the term in(3sqrt(((a)/(sqrt(b))) + (sqrt((b)/ (3sqrt(a))))^(21) ...

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  16. Using the binomial theorem, evaluate (102)^5 .

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  17. Find the 6th term in expansion of (2x^2-1/(3x^2))^(10)dot

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  18. Find a, if 17th and 18th terms in the expansions of (2+a)^50 are equal...

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  19. Find n , if the ratio of the fifth term from the beginning to the ...

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  20. Simplify: x^5+10 x^4a+40 x^3a^2+80 x^2a^3+80 x a^4+32 a^5dot

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