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

The lowest integer which is greater than $\left(1+\frac{1}{10^{100}}\right)^{10^{100}}$ is $.....$

The mean of the coefficients of $x, x^2, \ldots, x^7$ in the binomial expansion of $(2+x)^9$ is $...........$.

The total number of terms in the expansion of $(x+a)^{47}-(x-a)^{47}$ after simplification 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

Using the Binomial Theorem,determine which number is larger: $(1.1)^{10000}$ or $1000$.