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

Prove that `sum_(r = 1)^n r^3 ((C_r)/(C_(r - 1))^2) = (n (n + 1)^2 (n+2))/(12)`

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Prove that sum_(r = 0)^n r^3 . C_r = n^2 (n +3).2^(n-3)

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) .

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

Show that sum_(r=0)^(n) (-1)^(r ). ""^(n)C_(r ) {(1)/(2^(r )) +(3^(r ))/(2^(2r)) +(7^(r ))/(2^(3r)) +…."upto m terms"}=(2^(mn)-1)/(2^(mn)(2^(n)-1))

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. With usual notations prove that C1/C0 + 2. C2/C1 + 3.C3/C2 + ……+n.(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. 6th term of (3 + (2x)/(3))^(3//2)

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  18. Prove that : Write the general term in the expansion of (1-4x)^(-3)

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  19. Write the general term in the expansion of (3 - (5x)/(4))^(-1//2)

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  20. Find the coefficient of x^5 in (3 - 4x)^(-1)

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