GERMAN | A Nice Olympiads Trick | No Calculated Allowed

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[@RyanLewis-Johnson-wq6xs]

999001 final answer

[@CharlesChen-el4ot]

Ｉ 1:56 1:57 Let n = 1000
999 ^ 4 = (n - 1)^4
(n^4+ (n--1)^4+1)/(n^2 + (n - 1)^2+1)
(n^4+( n^2 -2n+ 1)^2 + 1)/(2*n^2-2n +2)
2* n^4 - 2* n^2*(2n-1)
+(2n=1)^2/2*(n^2-n+1)
2 * n^4 - 4*n^3+ 2n^2
+ 4n^2- 4n + 1
/ 2(n^2-n+1)
2^n4-4*n^3+6*n^2-4n+ 1/2(n^2-n+ 1)

[@RyanLewis-Johnson-wq6xs]

(100^6+999^2+1)/(100^3+999^2+1)=500500.498999500501000499 recurring