# Math induction with sigma notation

#### carameled

##### New member
Prove by math induction that

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

#### MarkFL

Staff member
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

##### New member
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?

#### MarkFL

Staff member
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

##### New member
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?

#### Country Boy

##### Well-known member
MHB Math Helper
Well, can you answer the question: is the statement true when n= 1?