2014 · Q32
What is 1/(a − b) − 1/(a + b) − 2b/(a² + b²) − 4b³/(a⁴ + b⁴) − 8b⁷/(a⁸ − b⁸) equal to?
Elementary MathematicsAlgebra
- Aa + b
- Ba − b
- C1
- D0
Explanation
Each pair telescopes: 1/(a−b) − 1/(a+b) = 2b/(a²−b²); combining successively with the next term doubles the numerator until 8b⁷/(a⁸−b⁸) − 8b⁷/(a⁸−b⁸) = 0.