Tasks in Ada are effective to speed up computations on multicore processors. In writing parallel programs we determine the granularity of the parallelism with respect to the memory management. We have to decide on the size of each job, the mapping of the jobs to the tasks, and on the location of the input and output data for each job. A multitasked Newton's method will show the effectiveness of Ada to speed up the computation of power series. This application belongs to the free and open source package PHCpack, a package to solve polynomial systems by polynomial homotopy continuation.