What are partial sums?
Ever wondered what a partial sum is? The simple answer is that a partial sum is actually just the sum of part of a sequence. You can find a partial sum for both finite sequences and infinite sequences.
When we talk about the sum of a finite sequence in general, we’re talking about the sum of the entire sequence. Because the sequence is finite, we can find the sum of the entire thing by adding all the terms together. When we talk about the sum of an infinite sequence, we’re talking about the sum of the entire sequence. But because an infinite sequence goes on forever, we have to use special tricks to find the sum of the whole thing. So we use a special name for the sum of an infinite sequence; we call it a “series”.
A partial sum, on the other hand, is just the sum of part of a sequence. In other words, we just take the sum of a few terms of the sequence to find the partial sum. For that reason, we can find the partial sum of either a finite sequence or an infinite sequence. Oftentimes, you’ll be asked to find the partial sum of something like the first five terms of the sequence. In which case, you simply add the first five terms together, and you’ve got the partial sum of the first five terms of the sequence.
00:18 // What is a sequence? What’s the difference between a finite sequence and an infinite sequence? How do you find the sum of a finite sequence or an infinite sequence?
01:12 // What are partial sums? What kind of sequence do you need in order to find a partial sum?
01:41 // How do you express a partial sum in summation notation? How do you expand the summation notation to show the partial sum?