If $a _ { 1 } = 1$ And $a _ { n + 1 } = \sqrt { 1 + a _ { n } }$

question 282

Multiple Choice

If $a _ { 1 } = 1$ and $a _ { n + 1 } = \sqrt { 1 + a _ { n } }$ for $n \geq 1$ and $\lim _ { n \rightarrow \infty } a _ { n } = L$ is assumed to exist, then what must $L$ be?

• A) \(\sqrt { 2 }\)
• B) \(\sqrt { 3 }\)
• C) \(\sqrt { 5 }\)
• D) \(\sqrt { 7 }\)
• E) \(\frac { 1 + \sqrt { 2 } } { 2 }\)
• F) \(\frac { 2 + \sqrt { 3 } } { 4 }\)
• G) \(\frac { 1 + \sqrt { 5 } } { 2 }\)
• H) \(\frac { 3 + \sqrt { 7 } } { 2 }\)

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IR Absorption

The process where a molecule absorbs infrared radiation, leading to vibrational transitions, used in spectroscopy to identify chemical compounds.

Intense IR Absorption

Refers to the strong absorption of infrared light by a molecule, typically due to specific bond vibrations, useful in identifying functional groups.