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An equation to organize perfect squares in a sequence.

I have created an equation, I do not know if it has been made before. It organizes all of the perfect squares into a sequence.

$$s_{n}=((sqrt(s_{n-1})*2)+1)+s_{n-1}$$ Please note, I made this as a result of boredom. This is my first time posting a note or equation, do not mind the formatting errors. $$s_{1}=1$$

Note by Ethan Molin
2 years, 6 months ago

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Interesting, I must have input the equation incorrectly. Thank you for notifying me of this. · 2 years, 6 months ago

Are you sure the equation is correct? I'm getting $$s_3 = 13$$. · 2 years, 6 months ago

I have corrected the error, thank you for informing me of this. · 2 years, 6 months ago

Essentially, $$\displaystyle (a+1)^2=(a^2+2a+1)$$. · 2 years, 6 months ago