Similar Posts

Subscribe
Notify of
3 Answers
Oldest
Newest Most Voted
Inline Feedbacks
View all comments
eterneladam
7 months ago

a(1) = 2

a(2) indicate the distance lying at the top of the hatched triangle, it is as long as half the base of this triangle, so according to Pythagoras

a(2) = 1/2 * Root(2 a(1)^2) = a(1) / Root(2)

General

a(n+1) = a(n) / root(2), or

a(n) = 2 / Root(2)(n-1)

The sum a(1) + a(2) + … then gives the geometric row

2 * Sum(n=0, infinite, 1 / Root(2)^n )

You should get that with the areas now.

gauss58
7 months ago

Entrance:

The triangles are at right angles.

The first triangle has the Kathete a_1 and the hypotenuse h_1 = a_1 * √2 (Pythagoras).

The hypotenuse h_1 is the catheter a_2 of the second triangle. Hypotenuse h_2 = 2 * a_1 (Pythagoras).

The hypotenuse h_2 is the catheter a_3 of the third triangle. Hypotenuse h_3 = 2 * a_1 * √2.

etc.

The adjacent lengths a_i differ in each case by the factor √2.

With this knowledge you should be able to solve the task.