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) 232 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