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## Main Question or Discussion Point

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 cant 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 cant just see why s2 is coming that way!!!!

Thanx