Answer:
Induction is done by demonstrating that if the condition is true for some n then it must also be true for n+1. If you then show that the condition is true for n=0 then it must be true for all n>0. For this problem:
Step 1: n=1
The sum of the first 1 odd numbers is 1. 12=1. Therefore the condition holds for n=1.
Step 2: induction
If the sum of the first n odd numbers is n2 then the sum of the first n+1 integers is n2+(2n+1)=(n+1)(n+1)=(n+1)2
So the condition is also true for n+1.
Step 3: conclusion
Since the we have shown that the condition is true for n=1 and we have shown that if it is true for n then it is also true for n+1 then it follows by induction that it is true for all n≥1.
Step-by-step explanation:
sorry if wrong
