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

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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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find a, if 17th and 18th terms in the expansions of (2+a)^50 are equal...

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

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  3. 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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  4. 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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  5. Find the approximation of (0. 99)^5 using the first three terms of its...

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

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

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

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

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

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

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

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

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  14. Find the last two digits of the number (23)^(14)dot

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  15. Find the last two digits of the number 27^(27)dot

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  16. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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  17. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

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  18. Using the binomial theorem (without using the formula for .^(n)C(r)), ...

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  19. Find the value of .^(4n)C0+^(4n)C4+^(4n)C8+...+""^(4n)C(4n) .

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  20. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

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