Look at the table. Make a conjecture about the sum of the first 30 positive numbers

Question

2 = 2 = 1•2

2+4 = 6 = 2•3

2+4+6 = 12 = 3•4

2+4+6+8 = 20 = 4•5

2+4+6+8+10 = 30 = 5•6

Answer 1

2+4+...+60=30*31 because the first multiplicand is the number of even numbers being summed and the second multiplicand is the next integer to it, so there are 30 even numbers and 31 follows 30. If we halve both sides of the equation we get the sum of the first 30 positive numbers (natural numbers or integers), according to the conjecture, so we would expect 31*30/2=465 to be the sum of the integers 1 to 30.