Induction Question (1 Viewer)

[Kujah]

In a room of 'n' people, they have to shake a hand with each other once. Prove by mathematical induction that the number of handshakes is 1/2 n(n-1) for n >= 2

Got to the first step.

Got stuck on the second and third

 

[undalay]

When n=k k(k-1)/2 as true.

We prove n=k+1

I.e we prove.
(k+1)(k)/2



When increasing the amount of people in the room from n=k to n=k+1, k hands must be shaken.

So we prove:

k(k-1)/2 + k = (k+1)(k)/2

LHS

k(k-1) + 2k / 2
= k^2 - k + 2k / 2
= k^2 + k /2
= k(k+1)/2

= RHS, as required.