- #1
ollybabar
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What is the algebra required to rewrite the nth term of: (sum from n=0 to infinity) of (pi^n)/(3^n+1) in geometric form?
Rewriting the nth Term of a Geometric Series with Algebra
- Thread starter ollybabar
- Start date
In summary, the conversation discusses the algebra required to rewrite the nth term of the infinite sum of (pi^n)/(3^n+1) in geometric form. The user also clarifies the meaning of "geometric form" and provides a rewritten version of the sum for easier understanding.
- #2
tiny-tim
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Welcome to PF!
Hi ollybabar! Welcome to PF!
(have a pi: π and an infinity: ∞ and try using the X2 tag just above the Reply box)
I don't understand your question …
what do you mean by "geometric form"? and so you mean the sum of the first n terms?
Anyway, it'll help if you rewrite it: (1/3) ∑ (π/3)n
Hi ollybabar! Welcome to PF!
(have a pi: π and an infinity: ∞ and try using the X2 tag just above the Reply box
)ollybabar said:
I don't understand your question …
what do you mean by "geometric form"? and so you mean the sum of the first n terms?
Anyway, it'll help if you rewrite it: (1/3) ∑ (π/3)n
- #3
ollybabar
- 3
- 0
I've figured it out; thanks for the reply though.
Related to Rewriting the nth Term of a Geometric Series with Algebra
1. What is a geometric series?
A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a fixed number called the common ratio. It follows the form a, ar, ar^2, ar^3, ... where a is the first term and r is the common ratio.
2. How do you recognize a geometric series?
A geometric series can be recognized by looking for a constant ratio between consecutive terms. If each term is multiplied by the same number, then it is a geometric series.
3. What is the formula for finding the sum of a geometric series?
The formula for finding the sum of a geometric series is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
4. How do you determine if a geometric series converges or diverges?
A geometric series will converge if the absolute value of the common ratio (|r|) is less than 1. If |r| is greater than or equal to 1, the series will diverge.
5. Can a geometric series have negative terms?
Yes, a geometric series can have negative terms as long as the common ratio is also negative. The terms will alternate between positive and negative, and the series may still converge or diverge depending on the value of the common ratio.
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