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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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Let (1 + x)^n= C_0+C_1x+C_2x^2+.....+C_n x^n and C_1/C_0+2 C_2/C_1+3 C_3/C_2+.....+ n C_n/C_(n-1)= (n(n+1))/k . The value of k is:

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : (1+C_1/C_0)(1+C_2/C_1)(1+C_3/C_2).... (1+C_n/ C_(n-1))=((n+1)^n)/(n!) .

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove that : C_0+ C_1/2 +C_2/3+.........+C_n/(n+1)= (2^(n+1)-1)/(n+1) .

Prove that C_0C_r+C_1 C_(r+1)+ C_2 C_(r+2)+...............+c_(n-r) C_n=((2n)!)/((n-r)!(n+r)!)

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : 2C_0+2^2 C_1/2+2^3 C_2/3+........+2^(n+1) C_n/ (n+1)= (3^(n+1)-1)/(n+1) .

Give that : C_1+2C_2 x+3C_3 x^2+.....+2n. C_(2n). x^(2n-1)=2n(1+x)^(2n-1) , where C_r=((2n)!)/(r !(2n-r)!) , r=0,1,2, ,2n , then prove that C_1^2-2C_2^2+3C_3^2-..........-2n C_(2n)^2=(-1)^n . nC_n .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0+1/3 C_2+1/5C_4+1/7C_6+.......... = 2^n/(n+1) .

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove the following : C_0C_n+C_1C_(n-1)+C_2C_(n-2)+.....+ C_nC_0= ((2n!))/(n!)^2 .

3C_0+3^2(C_1)/2+3^3(C_2)/3+.............3^(n+1)*(C_n)/(n+1) equal to

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. (2^1/3+1/3^1/3)^n if the ratio of 7th term from the beginning to the 7...

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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(3sqrt(((a)/(b))) + 3(sqrt((b)/ sqrt(a)))^(21) which h...

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  7. The coefficient of x^r [0lt=rlt=(n-1)] in the 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 then (sqrt(3)+1)^(2n) is necessarily divisible by

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  10. Find the solution of the following inequality 6 < 2x + 4 < 10

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

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  12. Solve the given inequality and show the graph of the solution on numbe...

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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 coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

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  15. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z^2+C2z^4++C(16)z^(32)...

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  16. Find the solution of the given inequality for real x x/3 > x/2 + 1

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  17. Find the solution of the given inequality for real x : x/2 + x/3 < 5

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  18. Find the solution of the following inequality for real x : 7x + 3 ge 4...

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  19. Solve the inequality 2 le 2x - 6 le 4

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  20. Solve the inequality 6 le 2x - 4 le 12

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