- #1
MAGNIBORO
- 106
- 26
hello, sorry for bad English, i have a question.
if we consider the following equations and we take natural values note that tend 2
x-1=0 -----------------> x = 1
x^2-x-1=0 -----------------> x = 1.618033988 (golden ratio)
x^3-x^2-x-1=0 -----------------> x = 1.839286755
x^4-x^3-x^2-x-1=0 -----------------> x = 1.927561975
x^5-x^4-x^3-x^2-x-1=0 -----------------> x = 1.965948236
x^6-x^5-x^4-x^3-x^2-x-1=0 -----------------> x = 1.983582843
then we can assume that when the equation has infinite terms the answer is 2.
and reaches the following "proof" and let me know if it's right:
1 image:https://gyazo.com/49a46e56fb19b4ec7aa21594e4e78cd1
2 image:https://gyazo.com/c6b99485e6d0271c1c0bbdbaaca29d54
Besides knowing if this is OK too I wonder if this is what is called "inductive method"
thanks.
if we consider the following equations and we take natural values note that tend 2
x-1=0 -----------------> x = 1
x^2-x-1=0 -----------------> x = 1.618033988 (golden ratio)
x^3-x^2-x-1=0 -----------------> x = 1.839286755
x^4-x^3-x^2-x-1=0 -----------------> x = 1.927561975
x^5-x^4-x^3-x^2-x-1=0 -----------------> x = 1.965948236
x^6-x^5-x^4-x^3-x^2-x-1=0 -----------------> x = 1.983582843
then we can assume that when the equation has infinite terms the answer is 2.
and reaches the following "proof" and let me know if it's right:
1 image:https://gyazo.com/49a46e56fb19b4ec7aa21594e4e78cd1
2 image:https://gyazo.com/c6b99485e6d0271c1c0bbdbaaca29d54
Besides knowing if this is OK too I wonder if this is what is called "inductive method"
thanks.
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