According to the geometric series 0.08 is the sum or state that the series diverges.
A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index . The more general case of the ratio a rational function of the summation index. produces a series called a hypergeometric series.
Given:
[tex]$\sum_{n=2}^{\infty} \frac{3^n}{12^n}$[/tex]
In the first term, it represents an unlimited geometric series.
b = 9/144
And the common ratio,
q = 3/12
By the ratio test ,it is convergent
Sum is
S = b/1-q
[tex]$=\frac{\frac{9}{144}}{1-\left(\frac{3}{12}\right)}$[/tex]
S = [tex]\frac{108}{1296}[/tex]
S = 0.08
To know more about Geometric series visit:
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The complete question is-
Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent seris).
[tex]$\sum_{n=2}^{\infty} \frac{3^n}{12^n}$[/tex]
