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anonymous
 5 years ago
what is the sum of all even numbers between 1 and 1000
anonymous
 5 years ago
what is the sum of all even numbers between 1 and 1000

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Owlfred
 5 years ago
Best ResponseYou've already chosen the best response.0Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sum of all even number between 1 and 1000 is 2+4+6.......................................998 a=2 d=2 an = a+ (n1)d 998= 2+n1)2 9982=(n1)2 996=(n1)2 488=n1 n=489 s489= 489/2[2+489] =489/2[491]=120049

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's the sum of all terms of the arithmetic progression, with a=2 and d=2. last term is 998 a=2 d=2 nth term = 998 998=a+(n1)d 998=2+(n1)2 998=2n n=499 sum=n/2(2a+(n1)d) therefore sum of 499 terms = 249500

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@shrishti, I think you made a slight error while calculating 996/2, which should equal 498, instead you have 488.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There are 500 even numbers first is 2 last is 1000 second is 4 last but one is 998 You will see (just like Gauss did ) that they both sum to 1002 So as there are 250 of these 'sums' ... 250 x 1002 = 250 500 This is a correct answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Another way of seeing this is sum from k =1 to k = 500 (2k) sorry about the lack of mathematics text.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{1}^{500}\] 2k hmmm still not good is it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0jacobmridul check your answer again the nth term is 1000

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@gianfranco, I'm afraid the question is sum of all even numbers "BETWEEN" 1 and 1000, in my humble understanding it excludes 1000. so the number of terms is 499 not 500.
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