 With the definition of the limit of a sequence, we can now also often define infinitary versions of the operations of addition and multiplication. For a finite number of terms, we define the ‘partial sum’ \(\sum_{i=1}^n a_i=a_1+\dots+a_n\) and ‘partial product’ \(\prod_{i=1}^{n} a_i=a_1\cdot\dots\cdot a_n\). For an infinite sequence of numbers \(a_n\), their infinite sum or product (when it is defined) is the limit of the partial sums or products: 