Asked by Janet

The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square.
a) find the sum of the areas all the squares

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


Answered by Reiny
the 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<sub>∞</sub> = 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.
Answered by Janet
so the perimeter is four and the series stay the same?
Answered by Reiny
Huh?
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?
Answered by Janet
yeah that is what I was asking...thanx.!
Answered by rushikesh
Good
Good
Answered by Lissy
Hi I don't understand the solution to the question, can you explain further?
Answered by Sakshi
That's ok but not good to understand .....
Answered by Dilip Sawale
Absolutely right and easy to understand
.
Answered by nhejneggr
whats 2+2
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