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. Show your work.Sn:    2 + 5 + 8 + . . . + ( 3n - 1) = n(1 + 3n)/2


Answer 1

S(1) = 2
by the formula: S(1) = 1(1 + 3)/2 = 2

S(2) = 2+5 = 7
by the formula: S(2) = 2(1+6)/2 = 7

S(3) = 2+5+8 = 15
by formula: S(3) = 3(1+9)/2 = 15

seems to work.

Answer 2

To show that it is true for any n, use your knowledge of some sums (k=1 to n):

sum(1) = n
sum(k) = n(n+1)/2

Now just simplify

3*sum(k) - sum(1)