Math induction with sigma notation

[carameled]

Prove by math induction that

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

 

[MarkFL]

I think what you mean is the induction hypothesis \(P_n\):

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

The first thing we want to do is confirm the base case \(P_1\) is true:

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

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 \(P_n\):

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

The first thing we want to do is confirm the base case \(P_1\) is true:

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

Is this true?

 

[MarkFL]

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?