$(a)\;\large\frac{n(n+1)}{2}+\large\frac{1}{9}\;(1-(0.1)^n)\qquad(b)\;n+\large\frac{1}{9}\;(1-(0.1)^n)\qquad(c)\;\large\frac{n(n+1)}{2}+\large\frac{1}{10}\;(1-(0.1)^n)\qquad(d)\;\large\frac{n(n+1)}{2}+\large\frac{1}{10}\;(0.1)^n$