00:01
In this problem, we are investigating a very interesting application of the comparison test and of conversion series, which is how we can formulate given decimals.
00:14
Because what we see is actually decimal places are just a different form or written differently of a series.
00:23
So we are given the decimal point d1, d2, d3, d4, continuing on for possibly infinitely many terms, that's what we're trying to figure out.
00:36
And we know this is equal to d1 over 10 plus d2 over 10 squared, plus d3 over 100 squared, and so to, pardon me, and 100 cubed, so on.
00:48
So what does that tell us? what can we do with this? well, that means that the decimal is written in a form that we can write as a series.
00:58
So what we can say is that this is the series from n equals 1 to infinity of d sub i over 10 raised to i, because what we saw was the term value, such as d sub 1, which is the same thing as 10 raised to the first in the denominator.
01:18
So now what we have to do is do a clever manipulation of these fractions in our series to find a series we know the conversions or divergence of to use the comparison test...