Sums II

Using the same method as Carl Friedrich Gauss did - pairing up the first and last numbers and multiplying by the number of pairs - we get: $(1 + 1000) \times \dfrac{1000}{2} = \boxed{500500}$

The formula for the sum of n numbers starting from 1 is

S[n] = n(n + 1)/2

Therefore,

S[1000] = 1000(1000 + 1)/2

= 500(1000 + 1)

= 500(1001)

= 500500

how to quickly to do it, add up the numbers 1 to 1000, The first stage, if 1 +2 +3 +4 +5 +6 +7 +8 +9 +10 = 50, then when summed 100 = 5050, if summed up 1000 = 500500, use the concept of logical thinking.

$\frac n2 \times(n+1)$

where: n is any positive number

$\frac {1000}{2} \times(1000+1)=500 \times 1001=\boxed {500500}$

n (n+1)/2 = 1000 ( 1000 + 1 ) / 2 = 500500

500500 n(n+1)/2

1+2+5 .. .. ..+n = n(n+1)/2

. 1 to 1000 = 1000(1001)/2=500500