Discussion Topic 3
A finite geometric series is the sum of a sequence of numbers. Take the sequence 1, 2,
4,8, for example. Notice that each number is twice the value of the previous
number. So, a number in the sequence can be represented by the function f(n) = 2n-1.
One way to write the sum of the sequence through the 5th number in the sequence
is In-12n-1. This equation can also be written as S5 = 2° + 21 + 22 + 23 + 24. If we
multiply this equation by 2, the equation becomes 2(55) = 21 + 22 + 23 + 24 + 25.
What happens if you subtract the two equations and solve for Ss? Can you use this
information to come up with a way to find any geometric series Sn in the form san-16h-1?