Question

prove statement by mathematical induction:
1+3+5+ ... + (2n-1)=n^2
I got up to
Let S={n is N: 1+3+5+ ... + (2n-1) = n^2}
Since 2(1) - 1 = 1^2 equation is true for n=1, thus 1 is S

Answer 1

Find your basis... let n = 1

then we need to find P(k)
next P(k+1)

Answer 2

I have to make S = N

Answer 3

1+3+5+ ... + (2k-1)=k^2

1+3+5+ ... + (2(k+1)-1)=(k+1)^2
1+3+5+ ... + (2k-1)=(k+1)(k+1)
1+3+5+ ... + (2k-1)=k^2+2k+1

Answer 4

I am getting there.. see that last line... to the right is your goal line.. your goal is to make the left look like k^2+2k+1

Answer 5

and I see it already if I do 1+3+5+...+(2k-1) + 2k+1 and subsitute that massive string with k^2

Answer 6

Since 1+3+5+ ... + (2k-1)=k^2

k^2 +2k + 1 = k^2+2k+1