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Prove that sum(r=0)^ssum(s=1)^n^n Cs^s C...

Prove that `sum_(r=0)^ssum_(s=1)^n^n C_s^s C_r=3^n-1.`

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

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

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

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

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

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

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

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

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

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

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  11. 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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  12. Find the value of (18^3+7^3+3.18.7.25) /(3^6+6.243.2+15.81.4+20.27.8+1...

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  13. Find the approximation of (0. 99)^5 using the first three terms of its...

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  14. If for n in N, underset(k=0)overset(2n)sum(-1)^(k)(.^(2n)C(k))^(2) = A...

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  15. There are two bags each of which contains n balls. A man has to sele...

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  16. Find the sum sum(i=0)^r.^(n1)C(r-i) .^(n2)Ci .

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  17. Prove that sum(r=0)^(2n)(r. ^(2n)Cr)^2=n^(4n)C(2n) .

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  18. If k and n are positive integers and S(k) = 1^(k) + 2^(k) + 3^(k) + "...

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  19. Prove that sum(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)(.^n Cr)=1/n .

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  20. Prove that (C1)/1-(C2)/2+(C3)/3-(C4)/4+....+((-1)^(n-1))/n Cn=1+1/2+1/...

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