M = 1/201 + 1/202 + 1/203 + ...... + 1/300
If we replace the first 99 terms by 1/300, then we get a sum = 100/300 = 1/3. Since the actual terms are larger than 1/300, the sum is larger than 1/3.
If we replace the all the 100 terms by 1/200, we get a sum = 100/200 = 1/2. Since the actual terms are smaller than 1/200, the sum is less than 1/2.
Therefore 1/3 < M < 1/2
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