SOLUTION: Find the sumΣ between n=1 and infinity for the expression 2(1/3)^n-1. The correct answer is one of the following. Which one. A) 3 B) 3/2 C) 6 D) 4/3 E) 4 F

Algebra ->  Sequences-and-series -> SOLUTION: Find the sumΣ between n=1 and infinity for the expression 2(1/3)^n-1. The correct answer is one of the following. Which one. A) 3 B) 3/2 C) 6 D) 4/3 E) 4 F      Log On


   

Question 1198602: Find the sumΣ between n=1 and infinity for the expression 2(1/3)^n-1.
The correct answer is one of the following. Which one.
A) 3
B) 3/2
C) 6
D) 4/3
E) 4
F) does not exist
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

        I believe that your sequence/expression is   2%2A%281%2F3%29%5E%28n-1%29.
        It is the only reasonable version for this context. 


Then the sequence is an infinite geometric progression with the first term of 2
and the common ratio  r = 1%2F3.


Use the standard formula for the sum of an infinite geometric sequence

    S = a%5B1%5D%2F%281-r%29.


In your case, it gives  S = 2%2F%281-1%2F3%29 = 2%2F%28%282%2F3%29%29 = 3.    ANSWER

Solved.

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In the future, use parentheses in your formulas, to show upper indexes ,
numerators and denominators for clear writing/reading.


In you case, the expression should be written in this form 2(1/3)^(n-1),

where the upper index (the degree) goes in parentheses.


Otherwise, tutors will have difficulties reading/interpreting your posts.