- #1
Blank101
- 16
- 0
Prove that S1, S2, S3 are true statements
1+3+5+...+(2n-1)=n^2
S1=1= (2(1)-1) = 1^2 True
S2=1+3 = (2(3)-1) = 5 which cannot= to the sum of our first 2 integers, which will make it false!
S3=1+3+5 = (2(5)-1) = 3^2 True
The problem is with S2 the book gave me an answer of 4=4 which is 2^2!
It also shows a different formula (n-1) = n^2
In my understanding of The mathematical induction a formula is usually given to prove an x number of integers, all those integers being proven true does not mean will be the same to all integers from the sequence. Thats when K+1 substitution comes in.
Can someone help me i know is a simple mistake but i can't just see why s2 is coming that way!
Thanx
1+3+5+...+(2n-1)=n^2
S1=1= (2(1)-1) = 1^2 True
S2=1+3 = (2(3)-1) = 5 which cannot= to the sum of our first 2 integers, which will make it false!
S3=1+3+5 = (2(5)-1) = 3^2 True
The problem is with S2 the book gave me an answer of 4=4 which is 2^2!
It also shows a different formula (n-1) = n^2
In my understanding of The mathematical induction a formula is usually given to prove an x number of integers, all those integers being proven true does not mean will be the same to all integers from the sequence. Thats when K+1 substitution comes in.
Can someone help me i know is a simple mistake but i can't just see why s2 is coming that way!
Thanx