Assume the statement is true for n=k . Prove that it must be true for n=k+1 , therefore proving it true for all natural numbers, n. Hint: Since the total number of dots increases by n each time, prove that . d(k) + (k+1) = d(k=1)

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)