Easy True or False Discrete mathematics question Easy True o

Easy True or False Discrete mathematics question

Easy True or False Discrete mathematics question If S = 1 + 2 + 3 ... + n then S = n(n+1)/2

Solution

True.

Prove by induction on n

Base case. n=1

1=1(1+1)/2=1

Hence base case is true

Inductive step

Assume it is true for n>=1 . We show that it is true for n+1

1+2+3+...n+(n+1)=n(n+1)/2+(n+1)=(n+1)(n/2+1)=(n+1)(n+2)/2

Hence true for n+1

Hence for all n

Hence proved.