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

Find the sum `sumsum_(0leiltjlen)"^nC_i`

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Find the sum (sumsum)_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j) .

Find the value of sumsum_(0leiltjlen) (""^(n)C_(i)+""^(n)C_(j)) .

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

The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(i-1)) is equal to

If (1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n , then show that the sum of the products of the coefficients taken two at a time, represented by sumsum_(0lt=iltjlt=n) ""^nc_i ""^n c_j is equal to 2^(2n-1)-((2n)!)/ (2(n !)^2)

The value of the expansion (sumsum)_(0 le i lt j le n) (-1)^(i+j-1)"^(n)C_(i)*^(n)C_(j)=

Find the sum sum_(k=0)^(15).^(30)C_k .

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

Find the value of underset(0leiltjlen)(sumsum)(-1)^(i-j+1)(.^(n)C_(i)*.^(n)C_(j)) .

Find the following sum: sumsum_(i ne j) ""^(n)C_(i).""^(n)C_(j)

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the sum (sumsum)(0leiltjlen) ""^(n)C(i).""^(n)C(j).

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

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

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

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

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

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

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

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

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  10. 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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  11. 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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  12. Find the approximation of (0. 99)^5 using the first three terms of its...

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

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

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

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

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

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

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

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  20. Prove that underset(r=0)overset(n)sum .^(n)C(r )sin rx. cos (n-r)x = 2...

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