perplexus.info :: Just Math : Sequence number compressed

Sequence number compressed (Posted on 2020-10-28)

Let there be a sequence with a₁=3/2 such that a_n+1=1+n/a_n. Find n such that 2020≤a_n<2021.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 5.0000 (1 votes)

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re: But...

Comment 7 of 7 |

(In reply to But... by Kenny M)

If a(n+1)=1+n/(a(n)) (The starting point is not that relevant for this purpose)

Then a(n + 1) = (a(n) + n)/a(n)

So a(n + 1)*a(n) = (a(n) + n)

Since a(n + 1) approximates to a(n) for large n, this is essentially the quadratic a(n)^2-a(n)-n = 0.

Edited on October 29, 2020, 9:11 pm

Posted by broll on 2020-10-29 21:05:39

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