jmc

We have $i^6=i^4\cdot i^2=1\cdot (-1)=-1$. We also have $i^{16}=(i^4{)}^4=1^4=1$, and $i^{-26}=1/i^{26}=1/(i^{24}\cdot i^2)=1/[1\cdot (-1)]=-1$. So, adding these three results gives $i^6+i^{16}+i^{-26}=-1+1-1=\boxed{-1}$.