Question

Discrete Math

Use mathematical induction to prove that for all positive integers n, 2 + 4 + ... + (2n) = n(n+1).

Answer 1

A solution to your problem has been given above.....

let, sn= 2 + 4 + ... + (zn), nEN. Suppose. Sn = n(n+1) for some NEN [le the result is SOLA Now, for n=1 Sn=s,= 2 = 1x 2 = n(n+1) So, the result is true for n=1. 9 true fou nen] Now, Sn+1 = 2+ 4+ + (2n) + 2(n+1). Snt 2 (n+1) n(n+1) + (n+1).2. [: Sn = n(n+1)]. = (n+1) (n+2) = Hinc Sn+1 = (n+1)(n+2). So, the result holds for (n+1) EN, whenever, the result holds for NEN. Hena, by principle of mathematical induction, we have, 2+4+-+(2n) = n(n+1), Vnen. (Proved).