The Three Square Problem

This original problem asks for the sum of the angles alpha, beta, and gamma, which has been proven to be 90 degrees. If the squares were lined up infinitely many times, creating infinitely many angles by drawing lines from the top left corner of the first square to the bottom right corner of each consecutive square, what would be the sum of all the angles?

#Calculus

Easy Math Editor

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`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`	$\sin \theta$
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Comments

This can be written as

$\sum_{n=1}^\infty \arctan\frac {1}{n}$

Which does not converge..

Krishna Sharma - 6 years, 8 months ago

But why not? The items in the sequence converge to 0 at infinity, so why doesn't the series converge?

Jason DeMuro - 6 years, 8 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}`	$\boxed{123}$