catsoup1230
New member
- Joined
- Sep 1, 2015
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Hi!
I am dreadful at math but I am sincerely wanting to understand the procedures for the following problems. I am hoping to improve my general idea of what to do so that I can repeat the methods on different problems as well.
I am specifically needing help on number 8 and number 12.
8. Discovery more Fibonacci relationship. By experimenting with numerous examples in search of a pattern, determine a simple formula for (Fn+1)2 - (Fn-1)2; that is, a formula for the difference of the squares of two Fibonacci numbers. (See Mindscape II.6 for a description of the notation Fn.)
12. Still more Fibonacci relationships. By experimenting with numerous examples in search of a pattern, determine a formula for Fn-1 + Fn+1; that is, a formula for the sum of a Fibonacci number and the Fibonacci number that comes after the next one. (Hint: The answer will not be a Fibonacci number. Try Mindscape II.10 first.)
7. Waiting for a nonprime. What is the smallest natural number n, greater than 1, for which (1 × 2 × 3 × ... × n) + 1 is not prime?
What I have done so far on number 8 is I tried to do (n+1) - (n-1) to create another F sub-something, but that got me F0 which always equals 1, and that doesn't make sense to me.
On number 12 I have tried to do a similar thing. (n-1) + (n+1) = 2n, so the entire equation equals Fsub2n.
Anyway that is all I have gotten so far.
Thanks so much ahead of time for the help!
I am dreadful at math but I am sincerely wanting to understand the procedures for the following problems. I am hoping to improve my general idea of what to do so that I can repeat the methods on different problems as well.
I am specifically needing help on number 8 and number 12.
8. Discovery more Fibonacci relationship. By experimenting with numerous examples in search of a pattern, determine a simple formula for (Fn+1)2 - (Fn-1)2; that is, a formula for the difference of the squares of two Fibonacci numbers. (See Mindscape II.6 for a description of the notation Fn.)
12. Still more Fibonacci relationships. By experimenting with numerous examples in search of a pattern, determine a formula for Fn-1 + Fn+1; that is, a formula for the sum of a Fibonacci number and the Fibonacci number that comes after the next one. (Hint: The answer will not be a Fibonacci number. Try Mindscape II.10 first.)
7. Waiting for a nonprime. What is the smallest natural number n, greater than 1, for which (1 × 2 × 3 × ... × n) + 1 is not prime?
What I have done so far on number 8 is I tried to do (n+1) - (n-1) to create another F sub-something, but that got me F0 which always equals 1, and that doesn't make sense to me.
On number 12 I have tried to do a similar thing. (n-1) + (n+1) = 2n, so the entire equation equals Fsub2n.
Anyway that is all I have gotten so far.
Thanks so much ahead of time for the help!
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