For any positive integer n, the sum of the first n positive

To both Experts: Thank you very much, helpful as usual

Hi Bunuel,

Plugging in number that's what helped me personally, but could you explain why general formula n(n+1)/2 doesn't work here? Is it because we include m and and and need to subtract these two terms? Than why do we do this exactly with the second part of the equation, not subtracting 1 from the 1st one and 1 from the second?

sum of the first n numbers: n(n+1)/2
sum of the first m numbers: m(m+1)/2

sum of the integers between m and n - excluding m and n:
m(m+1)/2 - n(n+1)/2
we can eliminate A and E right away, because the sign is +
C - is the sum of the integers between m and n, but without m and n so out.
E - clearly not correct, as it mixes m with n...

B

Can somebody please elaborate on how B is the option.Is the sum of integers between m and not equal to difference between sum of first m integers and sum of first n integers.I am not clear with this.Please explain

Missed this simple question because of over-confidence. Actually, it was more like - 'Is this really a GMAT type question?'

Anyhow, lesson - if you finish solving a question super quick, you need to check where the tricky part is.

I was confused about this as well, I think this is how it works:

If we're looking at the number of terms between 7 and 4, inclusive, we would use First - Last + 1 --> 7 - 4 + 1 = 4
Why do we add 1 here? Because we need to include the 4 (the terms are 7,6,5 AND 4).

It's the same idea here. Let's take m = 7 and n = 4, we're looking for the sum of first 7 ints - first 4 int:

7+6+5+4+3+2+1
-______4+3+2+1

In the problem, it says inclusive, so we must include the first and last ints in the set. In this case, we have to subtract 1 from n because otherwise we will remove the 4 (and thus part of the set that we need):

7+6+5+4+3+2+1
-________3+2+1

If we use n, n+1 we would actually end up removing even more of the terms. The idea is that we're looking for a chunk of sums between the biggest number and the smallest number, but we can't remove the smallest number so we have to make sure we subtract 1 less than that smallest number.

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