Sharon
level: college
I am a student

Hi,
Can you please help me with understanding this.

prove by induction: For every n>1, show that
2 + 7 + 12 + ...+ (5n-3) = n(5n-1)/2

I get so far and then get stuck with adding k+1 to both sides. I don't end up with what should be.

Help!

Hi Sharon,

In the inductive step I assumed that the expression is true for n = k, that is

2 + 7 + 12 + ...+ (5k - 3) = k(5k - 1)/2

I then want to use this assumption and prove the expression is valid when n = k + 1, which is

2 + 7 + 12 + ...+ (5k - 3) + (5(k+1) - 3) = (k+1)(5(k+1) - 1)/2.
The right side simplifies to (k + 1)(5k + 4)/2

Using the assumption that the expression is valid for n = k the left side becomes

2 + 7 + 12 + ...+ (5k - 3) + (5(k+1) - 3)
= k(5k - 1)/2 + (5(k+1) - 3)

Show that this simplifies to (k + 1)(5k + 4)/2

Penny