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Mathematics 18 Online
OpenStudy (anonymous):

find the sum of even integers between 1 and 60

OpenStudy (anonymous):

use a calculator and count it manualy.

OpenStudy (anonymous):

i think it's around >1000

OpenStudy (anonymous):

i mean <1000

OpenStudy (anonymous):

(60^2 + 60 )/2

OpenStudy (anonymous):

oops

OpenStudy (anonymous):

i am wrong

OpenStudy (anonymous):

all "even" would be (60^2 + 60) /4 ???

OpenStudy (anonymous):

There are 30 even integers between 1 and 60. The first and last pair add to 62. So there are 15 pairs of integers who's sum is 62. Therefore the total is 62 * 15 = 930

OpenStudy (nowhereman):

No, you are approaching this wrong. Even between 1 and 60 are 2, 4, 6, ..., 60 so 2*(1, 2, 3, ..., 30) thus you get the sum 2*30*31/2 = 30*31 = 930

OpenStudy (anonymous):

^ you are right, thanks for correction

OpenStudy (anonymous):

this is an arithmetic sequence of the following form a = 2n from n = 1 to n = 30. now use the formula for the arithmetic series: sum = (n/2) * (last term + first term) so sum = (30/2) * (2+30) = 480

OpenStudy (anonymous):

I think you mean 30/2 * (2+60)

OpenStudy (anonymous):

sorry sum = (30/2) *(2 + 60)

OpenStudy (anonymous):

930

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