Infinite geometric series - math problems
Number of problems found: 20
- Pilsen circus
The arrival of the circus in Pilsen was seen in the morning at 08:00 by a city citizen. He passed this information on 08:15 to three other residents of the city. Each of these three people then informed the other three residents at 08:30, and again at 08:
- Infinite decimal
Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless series of nines. Determine how much this number is less than the number 1. Thank you in advance.
- 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
- 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?
- 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?
- Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
- Decimal to fraction
Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
- 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+....
In a square with side 19 is inscribed circle, the circle is inscribed next square, again circle, and so on to infinity. Calculate the sum of the area of all these squares.
- Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 22 cm. Calculate: a) the sum of peri
Suppose on your 21st birthday you begin making monthly payments of $500 into an account that pays 8% compounded monthly. If you continue the payments untill your 51st birthday (30 years), How much money will be in your account? How much of it is interest?
- 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 ascend six minutes after takeoff? b) what is the overall height 10 minutes after launch
- 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?
- 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 tr
- Exponential decay
A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank?
- Fly and cyclist
Two cyclists are at 20 km apart on a same line. They start at same time towards each other at a speed of 10 km/hr. A fly sitting on one of the cyclists handle start flying towards the other cyclists at a speed of 20 km/hr. It touches the handle and move b
- Sum of GP members
Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
- Present value
A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years?