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Prove that (""^20C1)/(""^20C0) + 2. ...

Prove that
` (""^20C_1)/(""^20C_0) + 2. (""^20C_2)/(""^20C_1) + 3. (""^20C_3)/(""^20C_2) + …..+20. (""^20C_20)/(""^20C_19) = 210`

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1.""^20C_1 - 2.""^20C_2 + 3.""^20C_3 - …..-20.""^20C_20 =

(""^(20)C_(1))/(""^(20)C_(0))+2.(""^(20)C_(2))/(""^(20)C_(1))+3.(""^(20)C_(3))/(""^(20)C_(2)) +…20.(""^(20)C_(20))/(""^(20)C_(19)) =210

""^20C_0 + ""^20C_1 + ""^20C_2+…….+""^20C_10 =

""^20C_10.""^15C_0 + ""^20C_9.""^15C_1 + ""^20C_8.""^15C_2 + …..+""^20C_0.""^15C_10 =

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Prove that sqrt(3)"cosec"20^(@)-"sec"20^(@) =4 .

Show that ""^(10)C_2+^(11)C_2+^(12)C_2+^(13)C_2+...+^(20)C_2=^(21)C_3-^(10)C_3 .

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. With usual notations find the value of 3.C1 + 5.C2 + 7.C3 + ……….+n ter...

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  2. With usual notations prove that C1+2.C2x + 3.C3x^2 + ……+2n.C(2n) ...

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  3. Prove that (""^20C1)/(""^20C0) + 2. (""^20C2)/(""^20C1) + 3. (""^2...

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  4. If n is a positive integer and C4 = ""^nCr then find the value of sum(...

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  5. Prove that sum(r = 1)^(n+1) (2^(r +1) C(r - 1) )/(r (r + 1)) = (3^(n+...

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

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

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  8. If Cr denotes ""^nCr then show that C0 + (C1)/(2) + (C2)/(3) x^2 +...

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  9. If C0, C1, C2 ,……..Cn are the coefficient in the expansion of (1 + x)^...

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  10. With usual notations prove that C0 + 3.C1 + 3^2.C2 + ………..+3^n .Cn...

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  11. With usual notations prove that C1/C0 + 2. C2/C1 + 3.C3/C2 + ……+n.(...

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  12. Prove that (C0 + C1) (C1 + C2) …..(C(n-1) + Cn) = ((n+1)^n)/(n!) (C1.C...

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

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  14. Prove that following C(0)+(3)/(2).C(1)+(9)/(3).C(2)+(27)/(4).C(3)+……...

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  15. Find the range of x for which the binomial expansion of the following ...

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  16. Find the range of x for which the binomial expansion of the following ...

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  17. Find the range of x for which the binomial expansion of the following ...

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  18. Find the range of x for which the binomial expansion of the following ...

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  19. Find the set of values of x for which the binomial expansions of the f...

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  20. Find the set of values of x for which the binomial expansions of the f...

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