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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" [Broken]

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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