Given:
f(x)=Sum[x/n!] for all positive integers n, where the [] brackets define the integer part of x (e.g. [pi]=3)
What is x, if f(x)=1215
Using the insight from my previous (backward) attempt, the answer to this problem should be a bit above 1215/(e-1) = 707.1
Try 708:
708/1=708
708/2=354
708/6=118
708/24=29.5
708/120=5.9
and the integer parts sum to only 1214
If we do 709, the first addend increases by 1 but the others do not, so the solution is x=709. f(709)=1215
(x=710 will bump the first two addends up so f(710)=1217)
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Posted by Jer
on 2023-09-25 10:03:28 |
Better solution
