If we make a batch of parts, we can finish half of it in 18 days according to the plan. If we work for 3 days, the work efficiency will be improved by 1 / 8, how many days will it take

If we make a batch of parts, we can finish half of it in 18 days according to the plan. If we work for 3 days, the work efficiency will be improved by 1 / 8, how many days will it take

The original plan was to complete all the parts in 36 days, 1 / 36 of the parts in one day
3 / 36 = 1 / 12 in three days
Work efficiency increased by 1 / 8 = (1 / 36) × (1 + 1 / 8) = 1 / 32
3 + (1 / 3-1 / 12) / (1 / 32) = 11 days

One half of the plan can be completed in 18 days by making a batch of parts. If the work efficiency is improved by one third after three days, how long will it take to complete one third of this batch of parts

1. Work efficiency: 1 / 2 △ 18 = 1 / 36
2. The workload completed in 3 days: 1 / 36 × 3 = 1 / 12;
3. The remaining workload: 1 / 3-1 / 12 = 1 / 4
4. Later work efficiency: 1 / 36 × (1 + 1 / 3) = 1 / 27;
5. Time spent later: 1 / 4 △ 1 / 27 = 6.75 (days)
6. To complete 1 / 3 of this batch of parts, the time required: 6.75 + 3 = 9.75 (days)

1 × 1 / 2 + 2 × 1 / 3 + 99 × 1 / 100 + 100 × 101

=1 / 2 + 2 / 3 + 3 / 4 + 4 / 5 +. + 99 / 100 + 100 / 101 the top is regarded as 1, which is added to 100, and the bottom is 2, which is added to 101
The answer is 1