Let \(\displaystyle \ell{\{T\}}\) be the last digit of \(\displaystyle T\)
\(\displaystyle \ell{\{K\}}=\ell{\{n11^{n}\}}=\ell{\{n\}}\ell{\{11^n\}}\)
\(\displaystyle \ell{\{K\}}=\ell{\{n\}}=n-10int(\frac{n}{10})=10frac{\{\frac{n}{10}\}}\) ;; frac means fractional part