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Prove that sum(r = 0)^n r^2 . Cr = n (n ...

Prove that `sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)`

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Prove that sum_(r = 1)^(n+1) (2^(r +1) C_(r - 1) )/(r (r + 1)) = (3^(n+2) - 2n - 5)/((n+1)(n+2))

Prove that sum_(k=1)^(n-r ) ""^(n-k)C_(r )= ""^(n)C_( r+1) .

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sum_(r = 0)^(n-1) (C_r)/(C_r + C_(r+1)) =

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. If n is a positive integer and C4 = ""^nCr then find the value of sum(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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