Given the function is defined by, f(n)=1+0.6^{2}+0.6^{3}+0.6^{4}+0.6^{5}+...+0.6^{n-1}+0.6^{n }How can I define it in a more definite way and shorter? Help please!
You could write it as $\displaystyle \displaystyle \begin{align*} f(n) = \sum_{k = 0}^{n} \left( \frac{3}{5} \right) ^k - \frac{3}{5} \end{align*}$, and this sum is a finite geometric series, and so its sum can be found using the finite geometric series formula.