MHB Math induction with sigma notation

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The discussion revolves around proving the formula for the sum of a series using mathematical induction. The induction hypothesis is stated as the sum of \(3i + 1\) from \(i = 1\) to \(n\) equaling \(\frac{n}{2}(3n + 5)\). Participants emphasize the importance of confirming the base case, specifically checking if the formula holds true for \(n = 1\). There is some confusion regarding the induction hypothesis and the base case, highlighting a need for clarity on these concepts. The conversation ultimately seeks to establish the validity of the statement for the initial case.
carameled
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Prove by math induction that

n
sigma 3i + 1 = n/2 (3n + 5)
i = n
 
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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?
 
Wow, well I'm just asking for the prove with math induction. I don't understand any of that..
MarkFL said:
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 said:
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?
 
oh I was wrong, it is i = 1 , not i = n. my bad
MarkFL said:
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?
 
Well, can you answer the question: is the statement true when n= 1?
 

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