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March 2, 2015

March 2, 2015

Posted by **Janet** on Wednesday, March 18, 2009 at 7:53pm.

a) find the sum of the areas all the squares

b) find the sum of the perimeters of all the aquares

- Geomtric Series -
**Reiny**, Wednesday, March 18, 2009 at 8:25pmthe area of the first square is 1

clearly each successive square is 1/2 of the previous one.

check: side of second square:

(1/2)^2 + (1/2)^2 = x^

x^2 = 1/2

x = 1/√2

so the area = (1/√2)^2 = 1/2

so we have an infinite series

1 + 1/2 + 1/4 + ...

a=1, r=1/2

S_{∞}= 1/(1-r) = 1/(1-1/2) = 2

hint for b)

side of first square = 1

side of second square = 1/√2

....

take it from there.

- Geomtric Series -
**Janet**, Wednesday, March 18, 2009 at 8:34pmso the perimeter is four and the series stay the same?

- Geomtric Series -
**Reiny**, Wednesday, March 18, 2009 at 8:43pmHuh?

the perimeter of the first square =4

the perimeter of the second square = 4*(1/√2) = 4/√2

so a=4, r = 1/√2

sum = 4/(1 - 1/√2)

=

you finish it , ok?

- Geomtric Series -
**Janet**, Wednesday, March 18, 2009 at 8:53pmyeah that is what I was asking...thanx.!

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