Math Practice
Use S_n = a_1(1 − rⁿ)/(1 − r) for a finite sum and S = a_1/(1 − r) for an infinite one, which only exists when |r| < 1.
Find
Find the sum of the first 8 terms of
Find the sum of the infinite series
Does the infinite series
The ratio is 2, and
Find the sum of the first 6 terms of
Evaluate
Find the sum of the infinite series
Find the sum of the infinite series
Write the repeating decimal
It is
Write
A ball is dropped from 10 m and each bounce reaches 60% of the previous height. What total distance does it travel, in meters?
Down 10, then up and down
A salary starts at $40,000 and rises 3% each year. What is the total paid over 10 years, to the nearest dollar?
Mathematics verification: Mathematical formulas, calculations, worked examples and solutions are reviewed for accuracy before publication. How we check our work
These problems follow the geometric series lesson. Find the ratio first: it decides which formula to use and whether an infinite sum exists.
Only when the ratio is between −1 and 1. Then the sum is a_1 / (1 − r). Otherwise it diverges.
Write it as a geometric series. 0.777… is 0.7 + 0.07 + …, with r = 0.1, so it equals 0.7 / 0.9 = 7/9.
Type numbers without units or commas, and fractions like 7/9. For formulas, use n and ^ for powers, such as 3n - 1 or 5*2^(n - 1).