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If the coefficients of x^(9),x^(10),x^(1...

If the coefficients of `x^(9),x^(10),x^(11)` in expansion of `(1+x)^(n)` are in A.P., the prove that `n^(2)-41n+398=0`.

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

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

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

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

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

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

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