Problem: Find a positive integral solution to the equation
2+4+6+⋯+2n1+3+5+⋯+(2n−1)​=116115​.
Answer Choices:
A. 110
B. 115
C. 116
D. 231
E. The equation has no positive integral solutions.
Solution:
Sumbing the arithmetic progressions yields
116115​=2+4+⋯+2n1+3+⋯+(2n−1)​=n(n+1)n2​;116115​=n+1n​;n=115.