Infinite geometric series - examples

  1. Infinity
    circles-and-squares 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.
  2. Recursion squares
    squares_reccurent 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
  3. Fraction
    Gauss_stamp Fraction ? write as fraction a/b, a,b is integers numerator/denominator.
  4. To the cinema
    tree 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.
  5. Sum of series
    question Determine the 6-th member and the sum of a geometric series: 4+4/3+4/9+4/27+4/81+4/243+....
  6. Miraculous tree
    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?
  7. Decimal to fraction
    fractions_2 Write decimal number 2.864333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
  8. Hot air balloon
    balon 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
  9. Ten dices
    dices_3 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. Saving per cents
    penize.JPG The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
  11. Infinite decimal
    series 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.
  12. Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356

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