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. $s_{1}=1$

#NumberTheory

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Are you sure the equation is correct? I'm getting $s_3 = 13$ .

Siddhartha Srivastava - 6 years, 5 months ago

I have corrected the error, thank you for informing me of this.

Ethan Molin - 6 years, 5 months ago

Interesting, I must have input the equation incorrectly. Thank you for notifying me of this.

Ethan Molin - 6 years, 5 months ago

Essentially, $\displaystyle (a+1)^2=(a^2+2a+1)$ .

Satvik Golechha - 6 years, 5 months ago

Yes, but I was purposefully attempting to complete this without exponents.

Ethan Molin - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$