<p><span style="font-size:18px;"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-series-i" target="_blank">Series I Exercise</a></span></p><h2>What is a series?</h2>
<p>Basically the sum of the first $n$ terms of a sequence:</p>
<p>$$1, 2, 3, 4, ... \rightarrow \textrm{ sequence}$$</p>
<p>$$1 + 2 + 3 + 4 + ... \rightarrow \textrm{ series}$$</p>
<blockquote>
<p>For many people, "series" refers to summing up an infinitely large number of terms, and the term "partial sum" is used when summing up a finite number of terms. Since the GRE does not tend to focus too much on infinity, for the purpose of this entry, "series" can be thought of the same as a partial sum. We'll discuss more about infinite series in the next entry.</p>
</blockquote>
<h2>Solving series problems</h2>
<p>It depends on the type of problem. </p>
<ul>
<li>In many cases, you can just bruteforce. For example, if you're asked to find the sum of the first $6$ positive integers of $5$, it's easy enough to find the multiples and add them up together.</li>
<li>If you're dealing with an arithmetic sequence, you can use the ideas we've covered in the Arithmetic section of PrepSwift to find the sum (recall the concept of finding the sum of multiples over an interval). There's also a handy formula you'll see in the exercise of Series I that can make finding the sum of arithmetic sequences easy (and solve related problems).</li>
<li>If you're dealing with a geometric sequence, we'll see a formula for finding the sum in the exercise, but you are not expected to memorise the formula.</li>
<li>For other types of sequence, looking for a pattern can help. For example, if the sequence is $1$, $-1$, $2$, $-2$ and so on, notice that every alternating term cancels out. What do you think the sum of the sequence could be (hint: there are two, and one of them depends on the number of terms in the sequence)?</li>
</ul>