Question
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
a) find the sum of the areas all the squares
b) find the sum of the perimeters of all the aquares
Answers
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.
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.
Janet
so the perimeter is four and the series stay the same?
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?
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?
Janet
yeah that is what I was asking...thanx.!
rushikesh
Good
Good
Good
Lissy
Hi I don't understand the solution to the question, can you explain further?
Sakshi
That's ok but not good to understand .....
Dilip Sawale
Absolutely right and easy to understand
.
.
nhejneggr
whats 2+2