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C1/C0+2C2/C1+3C3/C2+............+nCn/C(n...

`C_1/C_0+2C_2/C_1+3C_3/C_2+............+nC_n/C_(n-1)=(n(n+1))/2`

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(C_(1))/(C_(0))+2(C_(2))/(C_(1))+3(C_(3))/(C_(2))+.........+n(C_(n))/(C_(n-1))=(n(n+1))/(2)

If (1+x)^(n)=C_(0)+C_(1)x+…..+C_(n)x^(n) , then (C_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1)) is :

(C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))(C_(3)+C_(4)).........(C_(n-1)+C_(n))=(C_(0)C_(1)C_(2).....C_(n-1)(n+1)^(n))/(n!)

C_(0)-(C_(1))/(2)+(C_(2))/(3)-............(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

prove that C_(0)C_(n)+C_(1)C_(n-1)+C_(2)C_(n-2)+.........+C_(n)C_(0)=2nC_(n)

C0-(C1)/(2)+(C2)/(3)-............+(-1)^(n)(Cn)/(n+1)=(1)/(n+1)

If quad (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n), then C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+...+C_(n-2)C_(n)=((2n)!)/((n!)^(2)) b.((2n)!)/((n-1)!(n+1)!) c.((2n)!)/((n-2)!(n+2)!) d.none of these

Let (1 + x)^(n) = sum_(r=0)^(n) C_(r) x^(r) and , (C_(1))/(C_(0)) + 2 (C_(2))/(C_(1)) + (C_(3))/(C_(2)) +…+ n (C_(n))/(C_(n-1)) = (1)/(k) n(n+1) , then the value of k, is

If (1+x)^n=C_0+C_1x+C_2x^2+C_3x^3+...+C_nx^n then prove that 2.C_0+2^2C_1/2+2^3C_2/3+2^4C_3/4+...+2^(n+1)C_n/(n+1)=(3^(n+1)-1)/(n+1)

ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Subjective Type Questions)
  1. Determine the term independent of a in the expansion of ((a+1)/(a^(2/...

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  2. If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coeffici...

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  3. Find n in the binomaial [ root (3)(2) + (1) /root(3)(3)]^(n) , if ...

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  4. if Sn = C0C1 + C1C2 +...+ C(n-1)Cn and S(n+1)/Sn = 15/4 then n is

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  5. C1/C0+2C2/C1+3C3/C2+............+nCn/C(n-1)=(n(n+1))/2

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  6. Find the term in (a/(sqrt(b))3+sqrt(b/(a3)))^(21) which has the same p...

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

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  8. Prove that if p is a prime number greater than 2, then the difference ...

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  9. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

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  10. Solve the equation ""^(11)C(1) x^(10) - ""^(11)C(3) x^(8) + ""^(11)...

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  11. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find th...

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  12. Evaluate sum(0 le i lne j le 10) ""^(21)C(i) * ""^(21)C(j).

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  13. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  14. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

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  15. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z2+C2z4++C(16)z^(32)t ...

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  16. If for z as real or complex . (1+z^(2) + z^(4))^(8) = C(0) C(1) z^...

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  17. Let f(x) = a(0) + a(1)x + a(2)x^(2) + …+ a(2n) x^(2n) and g(x) = b...

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  18. If a0,a1,a2,.... be the coefficients in the expansion of (1+x+x^2)^n ...

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  19. If a(0), a(1), a(2),… are the coefficients in the expansion of (1 ...

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  20. If a(0), a(1), a(2),… are the coefficients in the expansion of (1 ...

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