Math induction with sigma notation

Click For Summary

Discussion Overview

The discussion revolves around proving a mathematical statement using induction, specifically involving sigma notation. Participants are exploring the validity of the induction hypothesis and the base case for the summation formula.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant presents the statement to be proven by induction, suggesting a summation formula involving \(3i + 1\).
  • Another participant clarifies the induction hypothesis and proposes confirming the base case \(P_1\) to establish the proof.
  • Some participants express confusion regarding the induction hypothesis and the base case, indicating a lack of understanding of these concepts.
  • A participant acknowledges a mistake in the limits of summation, correcting it from \(i = n\) to \(i = 1\).
  • There is a request for confirmation of the truth of the statement when \(n = 1\), indicating a focus on the base case.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the understanding of the induction process, with some expressing confusion and others attempting to clarify the concepts involved. The discussion remains unresolved regarding the validity of the statement for the base case.

Contextual Notes

There are indications of missing foundational knowledge about mathematical induction among some participants, which may affect their ability to engage with the problem effectively.

carameled
Messages
3
Reaction score
0
Prove by math induction that

n
sigma 3i + 1 = n/2 (3n + 5)
i = n
 
Physics news on Phys.org
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?
 

Similar threads

Undergrad Mathematical Induction with Sigma notation
  • · Replies 5 ·
Replies
5
Views
4K
High School Variance & Standard Deviation
  • · Replies 42 ·
2
Replies
42
Views
6K
High School Sigma Multiplied Gaussian Distribution
  • · Replies 2 ·
Replies
2
Views
2K
High School Equation to approximate percent likelyhood of different sigma events
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Making Sense of Notation Confusion in Statistical Digital Signal Processing
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Discrete type normal distribution
  • · Replies 12 ·
Replies
12
Views
2K
Graduate A different discrete normal distribution
  • · Replies 2 ·
Replies
2
Views
2K
MHB Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples
  • · Replies 1 ·
Replies
1
Views
4K
High School Cosecant function: notation for the domain and range -- Am I right?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Proving First Order Logic in Machover's Text
  • · Replies 1 ·
Replies
1
Views
2K