\(M\left(x\right)=1+\left(-1\right)+\left(-1\right)^2+\left(-1\right)^3+\left(-1\right)^4+...+\left(-1\right)^{100}\)
\(=1+\left(-1\right)+\left(-1\right)^2+\left(-1\right)^3+\left(-1\right)^4+\left(-1\right)^5+...+\left(-1\right)^{98}+\left(-1\right)^{99}+\left(-1\right)^{100}\)
\(=1+\left(-1\right)+1+\left(-1\right)+1+\left(-1\right)+...+1+\left(-1\right)+1\)
\(=1\)
\(N\left(-1\right)=\left(-1\right)^2+\left(-1\right)^4+\left(-1\right)^6+\left(-1\right)^8+...+\left(-1\right)^{100}\)
\(=1+1+1+1+...+1\)
\(=50.1=50\)
\(M\left(-1\right)-N\left(-1\right)=1-50=-49\)
