- #1

carameled

- 3

- 0

Prove by math induction that

n

sigma 3i + 1 = n/2 (3n + 5)

i = n

n

sigma 3i + 1 = n/2 (3n + 5)

i = n

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- MHB
- Thread starter carameled
- Start date

- #1

carameled

- 3

- 0

Prove by math induction that

n

sigma 3i + 1 = n/2 (3n + 5)

i = n

n

sigma 3i + 1 = n/2 (3n + 5)

i = n

- #2

MarkFL

Gold Member

MHB

- 13,302

- 11

\(\displaystyle \sum_{i=1}^{n}\left(3i+1\right)=\frac{n}{2}(3n+5)\)

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?

- #3

carameled

- 3

- 0

\(\displaystyle \sum_{i=1}^{n}\left(3i+1\right)=\frac{n}{2}(3n+5)\)

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?

- #4

MarkFL

Gold Member

MHB

- 13,302

- 11

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?

- #5

carameled

- 3

- 0

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?

- #6

HOI

- 923

- 2

Well, can you answer the question: is the statement true when n= 1?

Share:

- Last Post

- Replies
- 5

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 312

- Last Post

- Replies
- 3

- Views
- 753

- Replies
- 7

- Views
- 364

- Last Post

- Replies
- 8

- Views
- 609

- Last Post

- Replies
- 3

- Views
- 85

- Last Post

- Replies
- 9

- Views
- 620

- Last Post

- Replies
- 1

- Views
- 648

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 1K