If the first term is 5/3 and the common difference is 1/3. Then the infinite sum of the geometric series will be 2.5.
The sum of sequence terms is a series. That is, it is a list of integers connected by addition operations.
The sequence is given in the form of a variable.
[tex]\rm a_n = 5 \left (\dfrac{1}{3} \right)^{n}[/tex]
The first term will be
[tex]\rm a_1 =\dfrac{5}{3}[/tex]
And the common ratio will be
[tex]\rm r =\dfrac{1}{3}[/tex]
Then the sum of the geometric series will be given as
[tex]\rm S_{\infty} = \dfrac{a_1}{1-r}\\\\\\S_{\infty} = \dfrac{5/3}{1-1/3}\\\\\\S_{\infty} = \dfrac{5/3}{2/3}\\\\\\S_{\infty} = \dfrac{5}{2}\\\\\\S_{\infty} = 2.5[/tex]
More about the series link is given below.
https://brainly.com/question/10813422
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Answer:
D. lim n->infinity 5/2(1-1/3^n)
Step-by-step explanation:
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