A number theory problem by Rithvik Gundlapalli

$\frac{1000^2+1000}{2}=5050$

here we have to implicate the below formula $\sum n=\frac{n(n+1)}{2}$ $=>\sum n =\frac{1000(1000+1)}{2}$ $=>\sum n=500 \times 1001$ $=> \sum=500500$ hence proved

S = 1 + 2 + 3 + ... + 998 + 999 + 1000

S = 1000 + 999 + 998 + ... + 3 + 2 + 1

2 S = 1000 (1001)

S = 500 (1001) = 500500

When you have to do a small version of this problem, like the sum of the numbers from 1 to 20, or even 30, it's possible to do it mentally or on paper. But when it comes to the bigger end of things, you have to use valuable formulas such as Gauss's Formula for Adding Consecutive Integers from 1 to n: [n ( n+1 )]/2.

[1000 ( 1000+1 )]/2 1000 x 1001 = 1001000 1001000 / 2 = 500500

So, 500500 is your answer!