# Infinite sum of areas

Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all triangles if the ABC triangle has a length? And?

Result

s =  1.732 a2

#### Solution: Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! #### To solve this verbal math problem are needed these knowledge from mathematics:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

## Next similar examples:

1. Miraculous tree Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?
2. Hot air balloon Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height which climbed in the previous minute. a) how many meters ascends six minutes after takeoff? b) what is the overall height 10 minutes after launch
3. Infinity In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
4. Recursion squares In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all
5. Fraction Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
6. To the cinema Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in.
7. Sum of series Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
8. Decimal to fraction Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
9. Ten dices When you hit ten dices at the same time you get average 35. How much do you hit if every time you get six, you're throwing the dice again?
10. Infinite decimal Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
11. Saving per cents The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
12. Series and sequences Find a fraction equivalent to the recurring decimal? 0.435643564356
13. Population growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
14. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected. Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors? A manufacturing firm purchased a heavy duty drilling machine. They were given two payment options: Option 1: Make a payment of \$46,000 immediately to settle the invoice for the machine. Option 2: Make a payment of \$21,500 immediately and the balance of \$