Final answer:
The correct answer is option B. A summation calculator is used to calculate the partial sums of a series. Solution A involves step-by-step manual calculation, while Solution B involves using functions of advanced calculators like the TI-83 and TI-84 series.
Step-by-step explanation:
The tool that can be used to calculate the partial sums of a series is a summation calculator. The term 'partial sums' refers to the sum of the first n terms of a series. For a series given by Sn = a1 + a2 + ... + an, the partial sum is the value of this expression for a particular value of n.
Solution A involves providing a step-by-step explanation of how to calculate the partial sums manually or with a basic calculator, showing how to add up each term in the series until the desired number of terms is reached.
Solution B involves using the function of advanced calculators like the TI-83, TI-83+, or TI-84, which have built-in capabilities to compute series and sequences, including partial sums. To use these calculators for summing a series, you typically use the 'sum(' function or the sigma notation available in their functions menu.
We can also consider additional options like online summation calculators, which generally allow you to input the general form of the terms in the series and the number of terms you want to sum over, automating the computation. Option C, a 'series convergence calculator,' is used to determine if a series converges and what it converges to, which is different from calculating partial sums. Option D, a 'sigma notation calculator,' can compute the sum of a series provided in sigma notation but isn't necessarily tailored specifically for partial sums.
The correct option for the tool that can calculate the partial sums of a series is B) Summation calculator.