sum of 1000 even integers

[westworld]

What is the formula for the sum of the first 1000 even integers. Or the sum of N even integers. I have seen several formulas but none make any sense. N(n+1) is n the number of integers =1000? If so would that be 1000(1001) =1001000?

 

[pka]

What is the formula for the sum of the first 1000 even integers. Or the sum of N even integers. I have seen several formulas but none make any sense. N(n+1) is n the number of integers =1000? If so would that be 1000(1001) =1001000?

The set \(\displaystyle \{2,4,\cdots,1998,2000\}\) contains the first one thousand even positive integers.
The sum of all those is \(\displaystyle \sum\limits_{k = 1}^{1000} {2k} = 2\sum\limits_{k = 1}^{1000} k = 2\frac{{1000 \cdot 1001}}{2} = 1000 \cdot 1001\)

 

[westworld]

thanks

Thanks for the reply.