Here is the problem that I'm having trouble with:
Rewrite each series in a sigma notation and find its sum.
1+.09+.81+...
I have no idea how I find the common difference or ratio in that one.
I don't think you will be able to do it with just those three terms.
perhaps you meant to type
1 + .09 + .0081 + ...
otherwise I agree with bob
If so, then
sum = [sigma] (.09)^(i-1) , i goes from 1 to infinity.
use S(infinity) = a/(1-r)
To rewrite the series in sigma notation, we need to find the pattern and the formula for each term. In this case, we can observe that each term is obtained by multiplying the previous term by 0.09.
Let's break it down step by step:
First term: 1
Second term: 1 * 0.09 = 0.09
Third term: 0.09 * 0.09 = 0.09^2 = 0.081
Fourth term: 0.081 * 0.09 = 0.09^3 = 0.0729
From the pattern, we can see that each term is calculated by multiplying the previous term by 0.09. So, the general formula for each term is 0.09^(n-1), where n represents the term number.
Now, let's express the series in sigma notation:
∑ (0.09^(n-1))
The sigma symbol, ∑, represents the sum of a series. The expression inside the parentheses represents the general formula for each term, and the summation is taken from n = 1 to infinity. The starting value of n depends on the position of the term in the series.
To find the sum of the series, we need to evaluate the expression. However, this particular series does not have a finite sum, as it goes on indefinitely. The terms keep getting smaller, approaching zero but never reaching it. We can say that the sum of this series is "undefined" or "divergent."
So, the sigma notation for the series is ∑ (0.09^(n-1)), but the sum is undefined.