Problem Statement
Using mathematical induction it is possible to prove the following inequality when n>1:int[] with 2 elements. Elements 0 and 1 denote the numerator and denominator of the return value, respectively, when written in least terms (reduced).
s = 13 + 23 + ... + (n-1)3 < n4/4 < 13 + 23 + ... + n3 = SGiven n return (S+s)/2 - n4/4 as a
Definition
- Class:
- InequalityChecker
- Method:
- getDifferences
- Parameters:
- int
- Returns:
- int[]
- Method signature:
- int[] getDifferences(int n)
- (be sure your method is public)
Constraints
- n will be between 2 and 100 inclusive.
Examples
2
Returns: { 1, 1 }
We have s = 1^3 = 1 S = 1^3 + 2^3 = 9 (S+s)/2 = (1+9)/2 = 5 n^4/4 = 16/4 = 4 Since 5-4 = 1, we return the fraction 1/1.
3
Returns: { 9, 4 }
We have s = 1^3 + 2^3 = 9 S = 1^3 + 2^3 + 3^3 = 36 (S+s)/2 = 45/2 n^4/4 = 81/4 We return the fraction 9/4.
100
Returns: { 2500, 1 }
Largest case.
4
Returns: { 4, 1 }
5
Returns: { 25, 4 }
6
Returns: { 9, 1 }
7
Returns: { 49, 4 }
8
Returns: { 16, 1 }
9
Returns: { 81, 4 }
10
Returns: { 25, 1 }
50
Returns: { 625, 1 }
33
Returns: { 1089, 4 }
79
Returns: { 6241, 4 }
25
Returns: { 625, 4 }
97
Returns: { 9409, 4 }
98
Returns: { 2401, 1 }
99
Returns: { 9801, 4 }
91
Returns: { 8281, 4 }
92
Returns: { 2116, 1 }
93
Returns: { 8649, 4 }
94
Returns: { 2209, 1 }
95
Returns: { 9025, 4 }
96
Returns: { 2304, 1 }