The conversation between human and AI assistant.
The sum of the first [math]n[/math] odd natural number is [math]n^2[/math], but what is the sum of first [math]n[/math] natural even number?
How do you derive that formula?
To derive the formula for the sum of squares of the first [math]n[/math] natural numbers, we can use mathematical induction. First, we prove that the formula holds true for [math]n=1[/math]. Then we assume that the formula is true for [math]n=k[/math] and we try to prove that it is also true for [math]n=k+1[/math].