# Math induction with sigma notation

• MHB
carameled
Prove by math induction that

n
sigma 3i + 1 = n/2 (3n + 5)
i = n

Gold Member
MHB
I think what you mean is the induction hypothesis $$P_n$$:

$$\displaystyle \sum_{i=1}^{n}\left(3i+1\right)=\frac{n}{2}(3n+5)$$

The first thing we want to do is confirm the base case $$P_1$$ is true:

$$\displaystyle \sum_{i=1}^{1}\left(3i+1\right)=\frac{1}{2}(3(1)+5)$$

Is this true?

carameled
Wow, well I'm just asking for the prove with math induction. I don't understand any of that..
I think what you mean is the induction hypothesis $$P_n$$:

$$\displaystyle \sum_{i=1}^{n}\left(3i+1\right)=\frac{n}{2}(3n+5)$$

The first thing we want to do is confirm the base case $$P_1$$ is true:

$$\displaystyle \sum_{i=1}^{1}\left(3i+1\right)=\frac{1}{2}(3(1)+5)$$

Is this true?

Gold Member
MHB
Wow, well I'm just asking for the prove with math induction. I don't understand any of that..

You don't understand what an induction hypothesis is, or demonstrating the truth of the base case? These are fundamental to induction. What method have you been taught?

carameled
oh I was wrong, it is i = 1 , not i = n. my bad
You don't understand what an induction hypothesis is, or demonstrating the truth of the base case? These are fundamental to induction. What method have you been taught?

HOI
Well, can you answer the question: is the statement true when n= 1?