# Infinite geometric series - examples

- Infinity

In a square with side 21 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. - Saving per cents

The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)? - Sum of series

Determine the 6-th member and the sum of a geometric series: 4+4/3+4/9+4/27+4/81+4/243+.... - Fraction

Fraction ? write as fraction a/b, a,b is integers numerator/denominator. - 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. - 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 8 days? - Decimal to fraction

Write decimal number 2.864333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures. - 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 = 31 cm. Calculate: a) the sum of perimeters of all - Series and sequences

Find a fraction equivalent to the recurring decimal? 0.435643564356 - 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

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