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With usual notations prove that C1/C0...

With usual notations prove that
`C_1/C_0 + 2. C_2/C_1 + 3.C_3/C_2 + ……+n.(C_n)/(C_(n-1)) = (n(n +1))/(2)`
Hence prove that
`(15C_1)/(15C_0) + 2.(15C_2)/(15C_1) + 3. (15C_3)/(15C_2) +……..+ 15. (15C_15)/(15C_14) = 120`

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AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. If C0, C1, C2 ,……..Cn are the coefficient in the expansion of (1 + x)^...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. 6th term of (3 + (2x)/(3))^(3//2)

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

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