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Math induction with sigma notation

carameled

New member
Aug 26, 2018
3
Prove by math induction that

n
sigma 3i + 1 = n/2 (3n + 5)
i = n
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,735
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
Aug 26, 2018
3
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

Administrator
Staff member
Feb 24, 2012
13,735
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
Aug 26, 2018
3
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
Jan 30, 2018
368
Well, can you answer the question: is the statement true when n= 1?