Use the Geogebra applet below to have a "race" between the partial sums for two different series. It is initially set up with the geometric series \({\sum\limits_{k = 1}^n {\left( {\frac{4}{5}} \right)} ^{k - 1}}\) versus the harmonic series \(\sum\limits_{k = 1}^n {\frac{1}{k}} \). Increase the number of terms n in the partial sum by using the slider. The best way to do that is to select "dot" on the slider and then use the right and left arrows on your keyboard. You can change the expression for either series...