Also \(\displaystyle (-1)^n =e^{i\pi n} =4\lfloor n/2 \rfloor -2n+1\).
Now the integer part can be expressed as infinite series . Floor Function -- from Wolfram MathWorld

Also \(\displaystyle (-1)^n =e^{i\pi n} =4\lfloor n/2 \rfloor -2n+1\).
Now the integer part can be expressed as infinite series . Floor Function -- from Wolfram MathWorld