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) $\frac { 3 + \sqrt { 7 } } { 2 }$

Question

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) $\frac { 3 + \sqrt { 7 } } { 2 }$

Quizplus · Accepted Answer

The Answer of 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) $\frac { 3 + \sqrt { 7 } } { 2 }$

If a1=1a _ { 1 } = 1a1​=1 And an+1=1+ana _ { n + 1 } = \sqrt { 1 + a _ { n } }an+1​=1+an​​

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