The discussion revolves around finding the limit of an infinite series, specifically the expression y = (2n + 3n) / 4n as n approaches infinity. Participants are exploring the behavior of this series and its components.
The discussion includes attempts to clarify the nature of the series and the limits involved. Some guidance has been offered regarding geometric series, while participants are also exploring the implications of decreasing areas in a different context. There is a mix of understanding and confusion regarding the convergence of these areas.
Participants are working under the constraints of homework rules, with one problem being a bonus question from a test. There is a noted lack of clarity in the second problem regarding what specifically is being summed or limited.
Dick said:It's 2^n/4^n+3^n/4^n=(2/4)^n+(3/4)^n. It's two separate geometric series. Can you deal with those?
steve2212 said:Ya I got that but I don't know how to find the sum of an infinite geometric series
steve2212 said:Oh sorry I'm stupid, I remembered how haha.
Since you're here I also have another hard one.
A circle is inscribed in a triangle, a square is inscribed in that circle, a circle is inscribed is that square, a pentagon is inscribed in that circle, the trend continues with the degree going up.
How do I proceed to solve this quesiton? I need to find t he sum of the limit
steve2212 said:The limit of the sum of the area. Sorry forgot that detail.
Dick said:How do you know the areas approach zero? Sure, they decrease. But that doesn't convince me that they approach zero. Do you know this has a simple solution? Because I'm sure not seeing it.
steve2212 said:Area can't be negative, and area decreases, it has to approach 0. Right?
steve2212 said:Sorry where do you get 1+ 1/n?