How can the sum of a Fibonacci series to the nth term be calculated?

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In summary, the conversation is about calculating the sum of a Fibonacci series to the nth term. The formula for this calculation is well known and can be found by researching Fibonacci numbers.
  • #1
heartyface
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hey:)
So I've been trying to calculate the sum of a fibonnaci series to the nth term...
like
a, b, a+b, a+2b, 2a+3b, 3a+5b, 5a+8b...
but then the series repeat themselves in this as well...
so
a1, a2, a3, a4, a5, a6...
is equal to
(excuse me for being uncapable of speaking latex the language of the gods...)
a1, a2, a1(a1)+a2(a2), a1(a2)+a2(a3), a1(a3)+a2(a4), a1(a4)+a2(a5)...
which is
a1, a2, a1^2+a2^2, a2(a1+a1^2+a2^2), a1^3+2a1a2^2+a1^2a2^2+a2^4...
(i could have made a mistake somewhere...)
so my point is
how... do you calculate the sum of a fibonnaci series to the nth term
thanks:)
 
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  • #2
Hey heartyface and welcome to the forums.

There is a formula for this and the process to derive the formula is a well known one (in the way that it has been known for a long time).

You should probably have a look at this [Google is your friend ;)]

http://en.wikipedia.org/wiki/Fibonacci_number
 

1. What is the sum of the first n terms in the Fibonacci series?

The sum of the first n terms in the Fibonacci series is equal to the (n+2)th term minus 1. This can be represented by the formula: S(n) = F(n+2) - 1, where S(n) is the sum and F(n) is the nth term in the series.

2. How is the Fibonacci series related to the golden ratio?

The ratio of any two consecutive numbers in the Fibonacci series approaches the golden ratio, which is approximately 1.618. As the numbers in the series get larger, the ratio between them gets closer to the golden ratio.

3. What is the significance of the Fibonacci series in nature?

The Fibonacci series can be observed in many natural phenomena, such as the branching of trees, the arrangement of leaves on a stem, and the spiral patterns in seashells and flower petals. This is because the Fibonacci sequence follows a growth pattern that is found in many living organisms.

4. How is the Fibonacci series used in finance?

The Fibonacci series is used in financial markets to identify potential support and resistance levels for a stock or market trend. Traders and investors use Fibonacci retracement levels to determine entry and exit points for trades based on the predicted patterns of price movements.

5. Can the Fibonacci series be extended beyond the traditional sequence?

Yes, the Fibonacci series can be extended beyond the traditional sequence by starting with different numbers. This is known as the general Fibonacci sequence and can be used to solve more complex mathematical problems. It can also be extended by adding more than two previous numbers to obtain the next number in the sequence.

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