Determine the value of the smallest positive integer N such that N1/N contains precisely one zero immediately following the decimal point.
Too easy?
How about seven zeroes, then?
A graphing calculator table shows
N N^(1/N)
38 1.100457444033732
39 1.098491064028148
so part 1's answer is 39.
Part 2:
After narrowing it down somewhat via calculator, the following code, actually at the first iteration of i, finds N = 190660033.957375 produces 1.0000001.
n1 = 190660000#: v1 = n1 ^ (1 / n1)
n2 = 190670000#: v2 = n2 ^ (1 / n2)
For i = 1 To 50
frac = (1.0000001 - v1) / (v2 - v1)
n1 = n1 + (n2 - n1) * frac
v1 = n1 ^ (1 / n1)
Text1.Text = Text1.Text & n1 & Str(v1) & crlf
DoEvents
Next
To narrow it down further, I used UBASIC under DOSBox, with more precision than what is shown below:
Immediate mode of UBASIC says
N = 190660033 produces 1.0000001000000006368
N = 190660034 produces 1.0000001000000001398
N = 190660035 produces 1.0000000999999996428
Part 2: answer is 190,660,035
Edited on December 4, 2014, 2:22 pm
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Posted by Charlie
on 2014-12-04 14:21:37 |
computer assisted solution
