MHB Math induction with sigma notation

Click For Summary
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
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?
 

Thread 'How do E[X] and E[|X|] relate?'

Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...
View full post »

Similar threads

Mathematical Induction with Sigma notation
  • · Replies 5 ·
Replies
5
Views
4K
B Variance & Standard Deviation
  • · Replies 42 ·
2
Replies
42
Views
5K
B Sigma Multiplied Gaussian Distribution
  • · Replies 2 ·
Replies
2
Views
2K
I Making Sense of Notation Confusion in Statistical Digital Signal Processing
  • · Replies 6 ·
Replies
6
Views
2K
A Discrete type normal distribution
  • · Replies 12 ·
Replies
12
Views
2K
A 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
3K
MHB Sequence of b_{k} with Explicit Formula: Proving by Math Induction
  • · Replies 2 ·
Replies
2
Views
1K
MHB Proving First Order Logic in Machover's Text
  • · Replies 1 ·
Replies
1
Views
1K
I Help understanding conditional expectation identity
  • · Replies 1 ·
Replies
1
Views
2K