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If an=sum(r=0)^n1/(nCr), then sum(r=0)^n...

If `a_n=sum_(r=0)^n1/(nC_r),` then `sum_(r=0)^n r/(nC_r)` equals

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If n-1Cr=(k^2-3)^nC(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, s...

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  2. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((^n Cr)/(^(r+3)Cr))

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  3. If an=sum(r=0)^n1/(nCr), then sum(r=0)^n r/(nCr) equals

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  4. The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a ...

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  5. Find ((dy) /dx) of sin(costheta) is

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  6. In the binomial expansion of (a-b)^n,ngeq5, the sum of the 5th and 6t...

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  7. Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(...

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  8. Given positive integers r gt 1, n gt 2 and that the coefficient of (3...

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  9. The coefficient of x^4 in (x//2-3//x^2)^10 is a.(405)/(256) b. (504)/(...

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  10. If Cr stands for nCr, then the sum of the series (2(n/2)!(n/2)!)/(n...

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  11. The sum underset(m)overset(i=0)sum ({:(10),(i):})({:(20),(m-i):}), (wh...

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  12. The coefficient of X^24in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)

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  13. The term independent of a in the expansion of (1+sqrta+ 1/(sqrta-1))^-...

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  14. The coefficient of x^(53) in the expansion sum(m=0)^(100)^100Cm(x-3)^(...

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  15. The coefficient of the term independent of x in the exampansion of ((x...

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  16. In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is ^40C4 ...

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  17. If coefficient of a^2 b^3 c^4 in(a+b+c)^m (where n in N) is L(L != 0)...

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  18. The last two digits of the number 3^(400) are: (A) 81 (B) 43 (C) ...

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  19. The expression (sqrt(2x^2+1)+sqrt(2x^2-1))^6 + (2/(sqrt(2x^2+1)+sqrt(2...

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  20. The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+...

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