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The domain of the function $\left[ 2tan\left( \pi x \right) \right]^{{log_{\left[ 2tan\left( \pi x \right) \right]}}\left( g\left( x \right)\right)}$, where $g(x)=\left( \frac{x^{2}+2x-3}{4x^{2}-4x-3} \right)$ contain the interval $[n+\frac{1}{4},n+\frac{1}{2})$, where $n$ is an integer. Then $n$ can be equal to (Note: [.] denotes greatest integer function)

The value of $\sum_{n=2}^{1947}\frac{1}{2^n+\sqrt{2^{1947}}}$ is equal to