Infinite geometric series - practice problems
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 - Determine 4113
Determine the sum of an infinite series: 1/3 + 1/9 + 1/27 + 1/81 ... - Decimal to fraction
Write the decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures. - 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)? - Fraction
Fraction frac(0, overline(38))(0,38) 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+.... - Remainder 34441
Find the remainder after division when we divide the sum of 1! +2! +3! +. ... . +300! number 13. - Quantities 60183
Determine the remaining quantities in the finite geometric sequence, given: n = 4, an = 12.5, sn = 187.5, a1 = ?, q =? - 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. - Determine 81988
Determine s5 of the geometric sequence if: a1 + a2 = 10 and a4 - a2 = 120 - Equation 6738
Solve the given equation in the set N: 1 - x + x² - x³ + x4 - x5 +…. + = 1/3 - Flower series
Every day, the flower develops two new flowers, and each of these new blossoms also bears two flowers each day. After eight days, how many blooms are already present in the garden? - Geometric series
How many terms of the geometric series 8+4+2+1+0.5+... must be taken for the sum to get within 10 to the power minus 4 of its sum to infinity? - Saving per cents
The first day I saved 1 cent and every following day a cent more. How many do I save in one year (365 days)? - Descending 81797
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence. - 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? - Triangular 81985
Trainees stand on the marks in rows exactly 1.5 m apart. They form an expanding triangular wedge (in each subsequent row, there is one more exerciser), while the distance between the front exerciser and the back row is 30 m. Determine the number of traine - Annual interest
A loan of 10 000 euros is to be repaid in annual payments over ten years. Assuming a fixed 10% annual interest rate compounded annually, calculate: (a) the amount of each annual repayment (b) the total interest paid. - Single-celled 4642
- 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?
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