What is 1+2+3...300 using the formula: s=n(n+2)/2?

Question

This is a mathematical equation

Answer 1

Several people have already provided your answer 45,150; and they've corrected the formula to use n+1 instead of n+2.

The interesting thing to me is, why does that formula work? There are 300 numbers. You can pair them up in this manner: (1+300) + (2+299) + (3+298) + ... + (149+152) + (150+151).

Each of these pairs adds up to 301, which is n+1. And there are 150 such pairs, which is n/2.

Your sum is 150 pairs times the 301 sum for each pair. That's 45,150 and the formula is n/2 times n+1 = n(n+1)/2.

And that's why the formula works.

Having done this, you can generalize the pairing procedure to get the formula for any arithmetic series. Instead of starting with 1, suppose you had the sum

5 + 8 + 11 + 14 + ... + 29 + 32 = ?

The first term of the beginning is 2 (5-3 = 2) and the common difference is 3. From (32-2)/3 = 10, there are 10 terms (and 5 pairs). If you pair it up, you get

(5+32) + (8+29) + ... + (17+20) = 5 x 37 = 185

From an example like this, you can get the general formula for the sum of an arithmetic series. As part of that, you'd want to figure out what to do if you have an or number of terms.

So from your question, you can get quite a bit more out of it.

Answer 2

You've *almost* got the right formula... to find the sum (represented as s) of all the numbers from 1 to some upper limit we'll call n, you can use the formula s = n(n + 1)/2. Notice that's "n+1," not "n+2."

So we plug in n=300 and we get:

s = (300)(300+1)/2
s = 150(301) [dividing 300/2 gives 150]
s = 45,150

Hope that helps!

Answer 3

It's actually s=n(n+1)/2

s = 300(301)/2 = 150(301) = 150(300)+150(1) = 45000 + 150 = 45150

Answer 4

you already have the formula which I believe is correct.

sum= (300/2)(300+1)
= 150(301)
=45150

Answer 5

n=300
s=300(300+2)/2

s=45,300

but wait, is that the correct formula?

no the formula is: S = [n * (n+1) / 2]


so s=45,150

Answer 6

the formula for sum of n natural nos. is
sum=n(n+1)/2
the formula given is s=n(n+2)/2.
n=300.
s=(n^2+2n)/2
s=(n^2+n+n)/2
s=n(n+1)/2 +n/2
s=sum+n/2
sum=s-n/2
s=300(302)/2
s=45300
sum=45300-150 (n/2=300/2=150)
sum=45150.

Answer 7

1 + 2 + 3 ... + n = ( (1 + 2 + 3 ... + n) +(n + (n-1) + (n-2) ... + 1 ) ) / 2
= ( (n+1) + (n+1) + (n+1) ... + (n+1) ) / 2
=n * (n+1)/2

add the number by itself and divide by 2.....