00:01
We've got the sum of this series from 1 to n.
00:03
Now, this is a bit of a problem, because if we want to solve for the sum of a series, we're used to having something of this form, where there is some term a1 multiplied by r to the k -minus 1.
00:15
Whereas here, we just have something to the k, not the k -minus 1.
00:21
But we can fix this.
00:22
Let's use some exponent rules here.
00:24
And so we know that if we have, for example, x to the y power, that is equal to x to the first power times x to the y minus one power.
00:36
So with this in mind, let's break up our two -thirds term.
00:40
That is, we can rewrite this as the sum from k equals 1 to n of two -thirds to the first power, which is just two -thirds, times two -thirds to the k -minus one power.
00:54
And now that has this form...