... k(k + 2) 1 − k k+2 for any positive integer k, so 1 1 1 + + + + + 15 35 63 99 14 3 1 1 1 + + + + + = × 3 × 5 × 7 × 9 × 11 11 × 13 1 1 1 = − + − + ··· + − 3 11 13 1 = × 1 = 13 13 Example 10 If ab ... 3x 5x − (1 + 3x) 15 − 2x + 16 − 2x =1 = = , 1 15 15 15 10 − 6x x 14 x − (10 − 6x) 10 − 13 x x 2x − − = − = , 2 14 14 x− it follows that 16 − 2x 10 − 13 x = , 15 14 14 (16 − 2x) = 15 (10 − 13 x), 224 ... + 1) (22 + 1) (24 + 1) · · · (22 + 1) + 10 = (22 − 1) (22 + 1) (24 + 1) · · · (22 + 1) + 10 = (24 − 1) (24 + 1) · · · (22 + 1) + 10 10 = · · · = (22 − 1) (22 + 1) + 10 10 11 = ((22 )2 − 1) + = 22·2...