The sum to $(n + 1)$ terms of the following series $\frac{{{C_0}}}{2} - \frac{{{C_1}}}{3} + \frac{{{C_2}}}{4} - \frac{{{C_3}}}{5} + $..... is

  • A

    $\frac{1}{{n + 1}}$

  • B

    $\frac{1}{{n + 2}}$

  • C

    $\frac{1}{{n(n + 1)}}$

  • D

    None of these

Similar Questions

The sum of coefficients in ${(1 + x - 3{x^2})^{2134}}$ is

The value of $-{ }^{15} C _{1}+2 .{ }^{15} C _{2}-3 .{ }^{15} C _{3}+\ldots \ldots$ $-15 .{ }^{15} C _{15}+{ }^{14} C _{1}+{ }^{14} C _{3}+{ }^{14} C _{5}+\ldots .+{ }^{14} C _{11}$ is

  • [JEE MAIN 2021]

The sum of the coefficients in the expansion of ${(1 + x - 3{x^2})^{2163}}$ will be

  • [IIT 1982]

$\frac{{{C_0}}}{1} + \frac{{{C_1}}}{2} + \frac{{{C_2}}}{3} + .... + \frac{{{C_n}}}{{n + 1}} = $

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