The reciprocal of every divisor of 24 is written down, and all of them are added together. What is the total?

The divisors are 1, 2, 3, 4, 6, 8, 12 and 24, and they add up to 60. Pair each divisor d with its partner 24 ÷ d: the reciprocal 1/d equals (24 ÷ d) ÷ 24, so the sum of the reciprocals is just (sum of all the divisors) ÷ 24 = 60 ÷ 24 = 5/2. Adding them one at a time agrees: 1 + 0.5 + 0.333… + 0.25 + 0.1667 + 0.125 + 0.0833 + 0.0417 = 2.5. Answering 60 gives the sum of the divisors themselves instead of their reciprocals.