Certainly! The nth triangle number is found by adding up the first n natural numbers. For example, the 4th triangle number is 1+2+3+4 = 10. The formula to find the nth triangle number is T_n = n(n+1)/2.

We can prove this formula by using mathematical induction, which is a way of showing that a formula is true for all values of n. To do this, we start by showing that the formula is true for n=1. Then, we assume that the formula is true for some value of k, and we use this assumption to show that the formula is also true for k+1. By doing this, we can show that the formula is true for all positive integers.

Using this method, we can prove that T_n = n(n+1)/2 is the correct formula for the nth triangle number.
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