Question

1+2+3+4+....+1002 use Gauss to Find the sum

Answer 1

gauss would say list the sequence in order, then under it list it again in reverse order and add each pair

1 + 2 + 3 + 4 +........... + 1002
1002 + 1001 +1000 + 999 + + 1
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1003 + 1003 + 1003 ....................... + 1003


so now many sums totalling 1003 do you have..?

Answer 2

4

Answer 3

no... if you are adding the numbers 1 to 1002 you will have 1002 things... and you know the sum of the pairs was 1003

now you added the sequence you have 2 sequences so you need to halve the answer to find the sum of 1.

so Sum = 1/2 x1002 x 1003