Vault Of Euclid

Limit of the Difference of Consecutive Square Roots

Polar coordinates warmup

\(a_{n}=\sqrt{n+1}-\sqrt{n}\)

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What you need first

Limits of sequences
Indeterminate forms
Multiplying by the conjugate
Difference of two squares

What this problem tests

Tests the ability to recognize the infinity minus infinity indeterminate form and apply the conjugate method to resolve it.

This is a classic introductory problem in calculus and real analysis courses when learning about sequences and indeterminate forms.

More on Polar coordinates

Sum of a Telescoping Series warmup
Convergence of an Alternating Series with Sine warmup
Convergence of a Series with an Exponential Denominator core

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