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If C0, C1, C2 ,……..Cn are the coefficien...

If `C_0, C_1, C_2 ,……..C_n` are the coefficient in the expansion of `(1 + x)^n` then show that
` C_0 C_r + C_1 C_(r + 1) + C_2 C_(r + 2) + ………..+ C_(n-r).C_n = ((2n)!)/((n-r)!(n+r)!)`

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AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. Prove that sum(r = 0)^n r^3 . Cr = n^2 (n +3).2^(n-3)

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Write down the first three terms in the expansion of (3 + x)^(-3//2)

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  16. Write down the first three terms in the expansion of (4 - 5x)^(-1//2)

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  17. Write down and simplify 5th term in the expansion of (6 + 7x)^(-2)

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  18. Write down and simplify 7th term in the expansion of (2 + 3x)^(-5)

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  19. Prove that : Find the 10^("th")" term of "(1-(3x)/(4))^(4//5)

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  20. Prove that : Find the 8^("th")" term of "(1-(5x)/(2))^(-3//5)

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