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
Since 7! = 5040 > 1215,
[x/n!] will only be non-zero for the n = 1,...,6.
1215+607+202+50+10+1=2085
Note this is reminiscent of the definition of e = sum(n=0 to inf) (1/n!)
so the answer is just a bit less than 1215(e-1)=2087.712 with difference only due to rounding down.
Edit: This is wrong. I found f(1215) instead of solving for f(x)=1215
Edited on September 25, 2023, 9:54 am
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Posted by Jer
on 2023-09-25 07:06:00 |
Solution
