Numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 Can it be expressed in an algebraic expression? Why?

Numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 Can it be expressed in an algebraic expression? Why?

Let A1 = 1, A2 = 3, and so on, it is easy to get an-an-1 = n, then an-1-an-2 = n-1. A3-a2 = 3, a2-a1 = 2, if the left and right sides of the above formula are superposed, an-a1 = n + n-1 + n-2 +. + 3 + 2 = (n + n-1 + n-2 +. + 3 + 2 + 1) - 1 = n * (n + 1) / 2-1, then an = (n ^ 2 + n) / 2

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