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Physicsissuef
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Homework Statement
Hi! After a tiring excursion, finally I am back...
Here is one for you:
In isosceles triangle ABC (triangle with all sides equal size) with side a, is drawn another isosceles triangle [itex]A_1,A_2,A_3[/itex] which points [itex]A_1,A_2,A_3[/itex] are in AB/2, BC/2, AC/2. Again third triangle with same attributes is drawn, fourth, fifth... infinite...
This looks like on this http://pic.mkd.net/images/404616untitled.JPG"
Find the sum of the perimeter and calculate the sum of the areas of the triangles.
Homework Equations
The Attempt at a Solution
I think it is something like this:
[tex]P + \frac{P}{4} + \frac{P}{8} + ... + \frac{P}{2^n}[/tex] for the area of the triangle, and
[tex]L + \frac{L}{2} + \frac{L}{4} + ... + \frac{L}{2^n^-^1}[/tex]
for the perimeter.
I think also, that I can write them as:
[tex]
P + \sum_{n=2}^n \frac{P}{2^n} = P + \frac{P}{4} + \frac{P}{8} + ... + \frac{P}{2^n}
[/tex]
[tex]
L + \sum_{n=2}^n \frac{L}{{2}^{n-1}} = L + \frac{L}{2} + \frac{L}{4} + ... + \frac{L}{{2}^{n-1}}
[/tex]
[tex]n \in \mathbb{N}[/tex]
[tex]n\geq 2[/tex]
n - number of triangles
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