Math induction with sigma notation

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SUMMARY

The discussion centers on proving the mathematical statement using induction, specifically the formula $$\sum_{i=1}^{n}(3i+1)=\frac{n}{2}(3n+5)$$. Participants confirm the base case \(P_1\) by evaluating $$\sum_{i=1}^{1}(3i+1)=\frac{1}{2}(3(1)+5)$$, establishing its truth. The importance of understanding the induction hypothesis and the base case is emphasized as fundamental concepts in mathematical induction. Clarifications regarding the correct indexing in the summation are also addressed.

PREREQUISITES
  • Understanding of mathematical induction
  • Familiarity with sigma notation
  • Basic algebra skills
  • Knowledge of evaluating summations
NEXT STEPS
  • Study the principles of mathematical induction in detail
  • Learn how to manipulate and evaluate sigma notation
  • Explore examples of induction proofs in various mathematical contexts
  • Practice solving summation problems involving algebraic expressions
USEFUL FOR

Students of mathematics, educators teaching algebra and calculus, and anyone interested in mastering mathematical proofs and induction techniques.

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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