00:01
To find the sum of this series, we recognize that it is a geometric sequence.
00:05
So when we have a geometric sequence, we can identify your first term.
00:09
So in this one, it would be a sum 1 is equal to 1.
00:12
Then we have a ratio.
00:14
What we're multiplying by repeatedly to get to that last answer there would be negative 3 over 4, because 1 times negative 3 4ths is negative 4ths.
00:24
Multiply again, you get the 9 .16th.
00:26
So then to find the sum of a geometric series like this, you would do a.
00:30
Sub 1, and then 1 minus r to the n, all over 1 minus r.
00:35
So as indicated by these exponents here, it looks like we're trying to find the sum of the first 34 digits here.
00:42
So a sub 1 here is 1, then we would have 1 minus, and then the negative 3 4ths for r, and the n would be 34...
