S3 is the 3rd partial sum, so we need to add the first 3 terms of the series. We get
S3 = 1 + 2 + 4 = 7.
Be Careful: To find Sn, we recommend writing the series in expanded form and ignoring the original indexing.
The original indexing of a series doesn't affect what its partial sums are. Whether a series is indexed starting at 0 or 1 or something else, S1 is the first term we see when we write the series in expanded form.