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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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Observation and maybe solution

| Comment 2 of 7 |

Exploring the series a bit in Excel led to a fortuitous observation that An^2-An+.5 seems to asymptotically approach n from below before An gets very large. Using this observation one gets:

If An=2020, n is very close to 4078380.5, therefore min n=4078381

If An=2021, n is very close to 4082420.5, therefore max n=4082420

4078381<=n<=4082420 may be the solution?

Not sure why the series leads to this relation? Anyone?

Posted by Kenny M on 2020-10-28 11:17:06

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