M is the sum of the reciprocals

Alternatively to improve understanding, we could think in terms of decimals as well.

The numbers of integers of M is (300 - 201) + 1 = 100
The sum of M starts at 0.005, while the remaining integers decrease until only 0.003333 is added.

Consider the following:
1/200 = 0.005
1/225 = 0.004444...
1/250 = 0.004
1/275 = 0.003636...
1/300 = 0.003333... (think of 1/3)

Now the sum includes less than one hundred 0.005's.
If we were given 100 0.005's we would have a total sum of 100*0.005 = 0.5 (= 1/2)

We receive more than one hundred 0.003333...'s
If we were given one hundred 0.0033...'s we would have a total sum of 100*0.003333... = 0.3333 ( = 1/3)

The sum of M has to be smaller than 0.5, but greater than 0.3333...
(1/3) < M < (1/2)

Oct 11, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Tayabur,

Good question! The reason we multiply by 100 each time is because we're considering two hypothetical situations:

1. All of the terms = 1/200
2. All of the terms = 1/300

This is to help us find the limits of M. Since there are 100 terms from 1/201 to 1/300, there would be 100 terms in both situations above. So, to find the sum if all 100 terms were equal to 1/200, we would add 1/200 100 times, which is equivalent to finding the product 100*(1/200). The same process could be followed replacing 1/200 with 1/300 in the second situation. :)

I hope this helps :D

Mar 23, 2016 • Comment

JESUS J Tellez

If one misses the state approach...ss there a relatively simple algebraic solution knowing it's an evenly spaced set? Average of first and last terms to equal average of set * # of items of set...?

Mar 10, 2016 • Comment

Mike McGarry, Magoosh Tutor

Aug 14, 2015 • Comment