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If n in N, then lim(nto oo)[sum(k=0)^(...

If n `in` N, then
`lim_(nto oo)[sum_(k=0)^(n)1/(k+1)(""^(n)C_(k))(ksum_(l=1)^(k)(""^(i)C_(k)))+1/(n+l)]^(1//n)` is equal to _______.

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MCGROW HILL PUBLICATION-MATHEMATICAL INDUCTION AND BINOMIAL THEOREM-SOLVED EXAMPLES ( Numerical Answer Type Questions)
  1. The sum of the coefficients in the expansion of (x^(2)-1/3)^(199)(x^(3...

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  2. sum(k=1)^(oo)sum(r=1)^(k)1/(4^(k))(""^(k)C(r)) is equal to=

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  3. If abne 0 and the sum of the coefficients of x^(7) and x^(4) in the ex...

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  4. If t(r) denotes the rth term in the expansion (x+1/x)^(23), and t(12)=...

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  5. The numbet of values of r for which the coefficients of rth and (r + 1...

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  6. Let t, denote the rth term in the binomial expansion of (1 + a)^(50). ...

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  7. If coefficient of x^(21) in the expansion of (1 + x)^(21) + (1 + x)^(2...

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  8. The number of irrational terms in the binomial expansion of (3^(1//5) ...

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  9. If the expansion of (3/7sqrtx-5/2(1)/(xsqrtx))^(13n) xgt0 contains a t...

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  10. The coefficient of the term independent of x in the expansion of ((...

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  11. The sum of the coefficients of all odd degree terms in the expansion o...

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  12. Let [x] denote the greatest integer less than or equal to x. If x=(sqr...

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  13. Coefficient of the term independent of x in the expansion of (1/2x^(1/...

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  14. If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i...

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  15. If sum(r=0)(n)(-1)^(r)(""^(n)C(r))/(""^(r+3)C(r))=3/(a+3) then (3a)/...

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  16. If n in N, then lim(nto oo)[sum(k=0)^(n)1/(k+1)(""^(n)C(k))(ksum(l=1...

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  17. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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  18. Let S be the sum of the last 24 coefficients in the expansion of (1 + ...

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  19. Let (1 + x)^(10)=sum(r=0)^(10)c(r)x^(r) and (1+x)^(7)=sum(r=0)^(7)d(r)...

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  20. If n ge 2, and (1 + x + x^(2))^(n) = a(0) + a(1)x + a(2)x^(2) + .. . +...

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