Math101: Use the induction to show that 1+2+3+..+n = n(n+1) / 2 Use the induction to show that 1+2+3+..+n = n(n+1) / 2 Quiz Forum 6/14/2020 Unifiedcamp 1 Answer(s) 775 views
Answers ( 1 )
Step1:p(1)
Step2: p(k)
Step3: p(k+1)
Step1: p(1) assume that n=1
RHS= n(n+1)÷2
1(1+1)÷2 =1(2)÷2 = 2÷2= 1
P(1) is true
Step2: p(k) is true by assumption, assume n=k
1+2+3+..+k=k(k+1)÷2
Step3: p(k+1)
Add k+1 to both sides
1+2+3+....+k+k+1= k(k+1)÷2 + k+1
(K+1) {k÷2 + 1÷1}
(K+1) {k+2÷2}
(K+1) {k+2}÷2
(K+1) {k+1+1}÷2
Assume n=(k+1)
n=(n+1)÷2
Peace67