In Wolfram Alpha:
simplify sqrt((n^3-(n-2)^3-2)/6)
leads, at the bottom of Alpha's solution, to an alternate form assuming n is real:
abs(n - 1)
n in this instance being 31415926535, z = 31415926535 - 1 = 31415926534
So this agrees with my original findings via
for n=10:20
a=n^3-(n-2)^3;
z=sqrt((a-2)/6);
disp([n a z])
end
n a z
10 488 9
11 602 10
12 728 11
13 866 12
14 1016 13
15 1178 14
16 1352 15
17 1538 16
18 1736 17
19 1946 18
20 2168 19
>>
with z showing up as n-1 all the way down.
so when n = 31415926535, z = 31415926534
Confirming that:
>> a=sym(31415926535)^3-sym(31415926533)^3
a =
5921762639938111518938
>> z=(sqrt((a-2)/6))
z =
31415926534
in Matlab
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Posted by Charlie
on 2022-04-17 08:24:58 |
solution
