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If a_1=1 and a_n+1=1+1/a^n for all n>1
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Updated on: 02 Jul 2024, 23:35

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If \(a_1=1\) and \(a_n+1=1+\frac{1}{a_n}\) for all \(n \geq 1\), which of the following is correct?

Indicate all correct options.

A. \(a_4>a_3\)

B. \(a_5>a_4\)

C. \(a_5=\frac{8}{5}\)

Indicate all correct options.

A. \(a_4>a_3\)

B. \(a_5>a_4\)

C. \(a_5=\frac{8}{5}\)

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Re: If a_1=1 and a_n+1=1+1/a^n for all n>1
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20 Feb 2024, 20:26

But wouldn't all, as in a1,a2,a3......, an, be equal to 1?

I just checked a1 = 1, gives us a2 = 1 and so on. Can you please clarify?

I just checked a1 = 1, gives us a2 = 1 and so on. Can you please clarify?

Re: If a_1=1 and a_n+1=1+1/a^n for all n>1
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02 Jul 2024, 22:36

How is C the answer? Could you pls explain Carcass

Pls check the RHS. It's "a squared".

dakshdhull wrote:

But wouldn't all, as in a1,a2,a3......, an, be equal to 1?

I just checked a1 = 1, gives us a2 = 1 and so on. Can you please clarify?

I just checked a1 = 1, gives us a2 = 1 and so on. Can you please clarify?

Pls check the RHS. It's "a squared".

If a_1=1 and a_n+1=1+1/a^n for all n>1
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02 Jul 2024, 23:41

Expert Reply

Aside the fact that I recognize the question in its latex code was completely upside down. I fixed now. I hope is fine.

Now

\(a_1=1

\)

If n =1 then \(a_2=1+\frac{1}{a_1}=1+1=2\)

If n=2 then \(a_3=1+\frac{1}{a_2}=1+\frac{1}{2}=\frac{3}{2}\)

If n=3 then \(a_4=1+\frac{1}{a_3}=1+\dfrac{1}{\frac{3}{2}}=1+\frac{2}{3}=\frac{5}{3}\)

If n=4 then \(a_5=1+\frac{1}{a_4}=1+\dfrac{1}{\frac{5}{3}}=1+\frac{3}{5}=\frac{8}{5}\)

A \(\frac{5}{3}>\frac{3}{2}\) Correct

B \(\frac{8}{5}>\frac{5}{3}\) Incorrect

C. \(a_5=\frac{8}{5}\) Correct

Now

\(a_1=1

\)

If n =1 then \(a_2=1+\frac{1}{a_1}=1+1=2\)

If n=2 then \(a_3=1+\frac{1}{a_2}=1+\frac{1}{2}=\frac{3}{2}\)

If n=3 then \(a_4=1+\frac{1}{a_3}=1+\dfrac{1}{\frac{3}{2}}=1+\frac{2}{3}=\frac{5}{3}\)

If n=4 then \(a_5=1+\frac{1}{a_4}=1+\dfrac{1}{\frac{5}{3}}=1+\frac{3}{5}=\frac{8}{5}\)

A \(\frac{5}{3}>\frac{3}{2}\) Correct

B \(\frac{8}{5}>\frac{5}{3}\) Incorrect

C. \(a_5=\frac{8}{5}\) Correct

gmatclubot

If a_1=1 and a_n+1=1+1/a^n for all n>1 [#permalink]

02 Jul 2024, 23:41
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