mattmannmf said:{sigma} 2*(-1/4)^(n-1)
Could i treat this as a geometric series? i know geometric is in the form of ar^n but the n is (n-1)
my A=2
my r= -1/4
A geometric series is a series of numbers where each term is found by multiplying the previous term by a constant value. For example, in the series 2, 6, 18, 54, ... the constant value is 3.
To solve a geometric series, you can use the formula: Sn = a(1-r^n)/(1-r), where Sn is the sum of the first n terms, a is the first term, and r is the common ratio between terms. You can also use the formula for the sum of an infinite geometric series, which is Sn = a/(1-r).
The expression 2*(-1/4)^(n-1) represents the general term in a geometric series where the first term is 2 and the common ratio is -1/4. This means that each term is found by multiplying the previous term by -1/4.
To find the sum of a geometric series using the expression 2*(-1/4)^(n-1), you would substitute the values of a=2 and r=-1/4 into the formula Sn = a/(1-r). This would give you the sum of the first n terms in the series.
Yes, a geometric series can have a negative common ratio. This will result in alternating positive and negative terms in the series. However, the series will only converge (have a finite sum) if the absolute value of the common ratio is less than 1.