Answer to Question #185250 in Discrete Mathematics for Evans

Question

Prove by induction that P(n): 2+3+3...+n=n(n+1)/2 Æn ≥ 1

Answer 1

Prove by induction that P(n): 1+2+3+4…+n=n(n+1)/2 Æn ≥ 1

Initial cases:

P(1) = 1 * 2 / 2 = 1

P(2) = 2 * 3 / 2 = 3

P(3) = 3 * 4 / 2 = 6

P(4) = 4 * 5 / 2 = 10

Let suppose that P(k) = 1 + 2 + … + k = k * (k + 1) / 2,

then P(k+1) should be (k + 1) * (k + 2) / 2

Using our assumption we will receive:

P(k+1) = 1 + 2 + … + k + k+1 = P(k) + k+1 = k * (k + 1) / 2 + 2 * (k + 1) / 2 = (k + 2) * (k + 1) / 2,

Answer: Proven.