- #1

- 107

- 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 [Broken]

2 image:https://gyazo.com/c6b99485e6d0271c1c0bbdbaaca29d54 [Broken]

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 [Broken]

2 image:https://gyazo.com/c6b99485e6d0271c1c0bbdbaaca29d54 [Broken]

Besides knowing if this is OK too I wonder if this is what is called "inductive method"

thanks.

Last edited by a moderator: