A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true.
Sn: 2 is a factor of n2 + 7n

Question

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. 
Sn:   2 is a factor of n2 + 7n

anonymous · Answer

$$Sn=n ^{2}+7n$$
$$S1=1^{2}+7\times1=1+7=8=2\times4,$$
which shows S1 is true.
$$S2=2^{2}+7\times2=4+14=18=2\times9$$
which shows S2 is true.
$$S3=3^{2}+7\times3=9+21=30=2\times15$$
which shows S3 is true.
Here S1,S2,S3 are all divisible by 2 ,hence all are true.

anonymous · Answer

You are the most awesome. Thanks!