From the natural numbers from 1 to 100, take two different natural numbers at a time and add them so that their sum is less than 100. How many different ways are there?

From the natural numbers from 1 to 100, take two different natural numbers at a time and add them so that their sum is less than 100. How many different ways are there?

∵1+98<100,1+97<100,… 1 + 2 < 100, 97 species; 2 + 97 < 100, 2 + 96 < 100 2 + 3 < 100, 95 species; 3 + 96 < 100, 3 + 95 < 100 3 + 4 < 100, a total of 93 species 48 + 51 < 100, 48 + 50 < 100, 48 + 49 < 100, a total of 3; 49 + 50 < 100, a total of 1, so 1 + 3 + 5 + +97 = 49 × 49 = 2401 species