The sum of coefficients in the expansion of $(1 + x + x^2)^n$ is

If $f(x)=(2011+x)^n$,where $x$ is a real variable and $n$ is a positive integer,then the value of $f(0)+f^{\prime}(0)+\frac{f^{\prime \prime}(0)}{2 !}+\ldots+\frac{f^{(n-1)}(0)}{(n-1) !}$ is

If $a$ and $b$ are distinct integers,prove that $a-b$ is a factor of $a^{n}-b^{n}$,whenever $n$ is a positive integer.

$(1 + x)^n - nx - 1$ is divisible by (where $n \in N$):

The sum of the coefficients in the expansion of $(1 + x - 3x^2)^{3148}$ is

The approximate value of $(1.0002)^{3000}$ is