Infinite geometric series - examples
- 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 tri
In a square with side 9 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.
- 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
Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
- 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.
- 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+....
- 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?
- 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
- Decimal to fraction
Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
- 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?
- 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.
- Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
- Series and sequences
Find a fraction equivalent to the recurring decimal? 0.435643564356
- 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?