The long question

Algebra Level 2

Calculate:

1+2+3+4+....1000000000.


The answer is 500000000500000000.

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2 solutions

You can use this formula to find the sum of 'n' terms of natural numbers. n ( n + 1 ) 2 \\ \\ \frac { n\quad *\quad (n+1) }{ 2 }

n = 1000000000

Therefore,

= 1000000000 ( 1000000001 ) 2 = 500000000 ( 1000000001 ) 1 = 500000000500000000 =\frac { 1000000000\quad *\quad (1000000001) }{ 2 } \\ =\frac { 500000000\quad *\quad (1000000001) }{ 1 } \\ =500000000500000000\\

Fred Fan
May 19, 2015

1+2+...100=5050, that's just 100/2 then put 2 50 in the front. 1+2+...1000=500500, it's the same thing, so 1+2+...1000000000=500000000500000000

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