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Sequence number compressed (Posted on 2020-10-28) Difficulty: 3 of 5
Let there be a sequence with a1=3/2 such that an+1=1+n/an. Find n such that 2020≤an<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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