Infinite geometric series - practice problems - last page
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 31
- Series and sequences
Find a fraction equivalent to the recurring decimal. 0.435643564356 - To the cinema
Jane at 8 AM got a message that all 1093 school pupils would 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 do all the scho - Miraculous tree The 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 it increase its height after 6 days?
- Ten dices
When you hit ten dice simultaneously, you get an average of 35. How much do you hit if every time you get six, you're throwing the dice again?
- Saving per cents
On the first day, I saved 1 cent, and I saved a cent more every following day. How much do I save in one year (365 days)? - Hot air balloon
A hot air balloon ascends 25 meters for a minute after launch. Every minute, it ascends 75 percent of the height it climbed in the previous minute. a) How many meters will ascend six minutes after takeoff? b) What is the overall height of the 10 minutes a - Decimal to fraction
Write the decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures. - Fraction
Fraction $e 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+....
- Infinity
A square with a side 19 long is an inscribed circle, and the circle is inscribed next to the square, 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 = 20 cm. Calculate: a) the sum of peri
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