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

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

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CENGAGE ENGLISH-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) "^nCi"^nCj

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  3. Prove that sum(r=0)^ssum(s=1)^n^n Cs^n 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 the 7th and 18th terms of the expansion (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+3xx18xx7xx25) /(3^6+6xx243xx2+15xx18xx4+20...

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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 ,sum(k=0)^(2n)(-1)^k(^(2n)Ck)^2=A , then find the value...

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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 a n d n are positive integers and sk=1^k+2^k+3^k++n^k , then prov...

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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+1/3++1...

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