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Proven Potential TMUA Sample Paper 1 · Q16

Paper 1Sequences & series

A sequence is defined by

an+1=11+an,a1=1.a_{n+1}=\frac1{1+a_n},\qquad a_1=1.

What is the value of ana_n as n→∞n\to\infty?

A15\frac1{\sqrt5}
B11
C1+52\frac{1+\sqrt5}{2}
D5−12\frac{\sqrt5-1}{2}
E1−52\frac{1-\sqrt5}{2}

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