Wow! I haven't seen an identity crisis like this in quite a while!!
Anonymous
Dr. Lexi
Crystal
Pablo
Maddie
Plus ... both Steve and Reiny already answered you on this:
http://www.jiskha.com/display.cgi?id=1457118310
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 is a factor of n2 + 7n
�
2 answers
Sn: 2 is a factor of n2 + 7n
n is either even or odd.
If n is even, n=2k
n^2 + 7n
= (2k)^2 + 7(2k)
= 4k^2 + 14k
= 2(2k^2 + 7k)
2 is a factor
If n is odd, n=2k+1
n^2 + 7n
= (2k+1)^2 + 7(2k+1)
= 4k^2+4k+1 + 14k+7
= 4k^2+18k+8
= 2(2k^2+9k+4)
2 is a factor
So, Sn is true
n is either even or odd.
If n is even, n=2k
n^2 + 7n
= (2k)^2 + 7(2k)
= 4k^2 + 14k
= 2(2k^2 + 7k)
2 is a factor
If n is odd, n=2k+1
n^2 + 7n
= (2k+1)^2 + 7(2k+1)
= 4k^2+4k+1 + 14k+7
= 4k^2+18k+8
= 2(2k^2+9k+4)
2 is a factor
So, Sn is true
2 answers