1,000

1 + 2 + 3 + 4 + 5 + + 999 + 1000 = ? 1+2+3+4+5+\cdots+999+1000 = \ ?


The answer is 500500.

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3 solutions

Hana Wehbi
Feb 16, 2020

n = 1 1000 n = n ( n + 1 ) 2 = 1000 ( 1001 ) 2 = 500500 \sum_{n=1 }^{ 1000} n =\frac{n(n+1)}{2} =\frac{1000(1001)}{2} =500500

Chew-Seong Cheong
Feb 16, 2020

This is a sum of arithmetic progression , which is given by S ( n ) = k = 1 n k = n ( n + 1 ) 2 \displaystyle S(n) = \sum_{k=1}^n k = \frac {n(n+1)}2 . For n = 1000 n=1000 , S ( 1000 ) = 1000 × 1001 2 = 500500 S(1000) = \dfrac {1000\times 1001}2 = \boxed{500500} .

1000 + 1 2 × 1000 \frac{1000+1}{2} \times 1000

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