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
$\frac{1}{{n + 1}}$
$\frac{1}{{n + 2}}$
$\frac{1}{{n(n + 1)}}$
None of these
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
The sum of the coefficients in the expansion of ${(1 + x - 3{x^2})^{2163}}$ will be
$\frac{{{C_0}}}{1} + \frac{{{C_1}}}{2} + \frac{{{C_2}}}{3} + .... + \frac{{{C_n}}}{{n + 1}} = $
The sum of all the coefficients in the binomial expansion of ${({x^2} + x - 3)^{319}}$ is