what is the fibonacci sequence and what is its relationship to the golden ratio?

http://www.google.com/search?q=fibonacci+golden+ratio&start=0&ie=utf-8&oe=utf-8&client=firefox-a&rls=org.mozilla:en-US:official

Many websites here that can help you -- especially the very first one from mathforum.org.

=)

The Fibonacci sequence begins
1,1,2,3,5,8,13,...
Each term after the second 1 is the sum of the previous two terms.
The golden number (or ratio) is (1+sqrt(5))/2 and is approxximately 1.6180339
The relationship of the Fibonacci sequence to the golden number is that if you take the ratio of the n-th term/(n-1)th term as n increases the limit of the ratio is the golden number. Thus in the sequence given above, consider the sequence of terms
2/1, 3/2, 5/3, 8/5, 13/8,...
That sequence of ratios of Fib. terms converges to the golden number. The last term , 13/8, is approx 1.625 Each term after that gets closer and closer to the gold. ratio.

i can't finish this h.w . because i can't find the factorzation for 293 and the h.w is due tomorrow!

293 is prime
test the divisor 2,3,5,7,11,13 and 17 to prove this.
Please post new questions or we'll miss your post.

To factorize a number, you need to find its prime factors. A prime factor is a prime number that divides the original number without leaving a remainder.

To check if a number is prime, you can start by dividing it by smaller prime numbers and see if any of them divide evenly.

In the case of 293, you can start by checking if it is divisible by 2. Since 293 is an odd number, it cannot be divisible by 2.

Next, you can check if it is divisible by 3. To do this, you can add up the digits of 293 (2 + 9 + 3 = 14) and see if the sum is divisible by 3. Since 14 is not divisible by 3, 293 is also not divisible by 3.

You can continue this process with other prime numbers such as 5, 7, 11, 13, and 17. If none of these prime numbers divide 293 evenly, then 293 is a prime number.

In this case, since none of the prime numbers tested divide 293 evenly, we can conclude that 293 is a prime number and cannot be factorized any further.

But don't worry! Remember that factorization is not always possible for all numbers. If you have any other questions or need further clarification, feel free to ask.