# Discrete Maths - Prove by induction

• Mar 11th 2013, 11:25 AM
lissy93
Discrete Maths - Prove by induction
Hey, I have several questions like this and really need some help on the first one so that I can get started. I'd be so grateful for an answer and some workings to be shown on this :)
The question I'm stuck on is:

Prove, by induction on n, that
2 + 5 + 8 + ..... + (3n - 1) = 1/2 n(3n + 1)
For all integers n >= 1

(The n>=1 part was meant to be: for n greater than or equal to 1. I couldn't find the symbol :/ )

Thanks in advance :)
• Mar 11th 2013, 11:28 AM
Plato
Re: Discrete Maths - Prove by induction
Quote:

Originally Posted by lissy93
Hey, I have several questions like this and really need some help on the first one so that I can get started. I'd be so grateful for an answer and some workings to be shown on this :)
The question I'm stuck on is:
Prove, by induction on n, that
2 + 5 + 8 + ..... + (3n - 1) = 1/2 n(3n + 1)
For all integers n >= 1

Have you done any work on this whatsoever?
At least you could post the base case.
• Mar 11th 2013, 11:32 AM
lissy93
Re: Discrete Maths - Prove by induction
Yeah I have don work on this, I have been reading about it all afternoon, I understand the theory, but not sure how to go about in answering the questions, how do I lay it out/ what information do I need to show/ how far do I need to go/ how much detail - I'm not really sure if I get the question - I'm not very good at maths, sorry if it is a stupid question to be posting :/
• Mar 11th 2013, 12:09 PM
peysy
Re: Discrete Maths - Prove by induction
three steps: 1-st - any "n", for example n=3 - 2+5+8=15=1/2*3*10=15 - correct<br>
2-nd - suggest that is correct for some integer n<br>
3-rd - prove it for n+1: 2+5+8+...+(3n-1)+(3*(n+1)-1)=1/2*(n+1)*(3n+4)=1/2n(3n+1)+(3n+2) end of the proof
• Mar 11th 2013, 01:45 PM
emakarov
Re: Discrete Maths - Prove by induction
See this description of a proof by induction. For sample proofs, see, e.g., here or here. Then try to adapt these proofs to your situation. Better yet, see examples of proof by induction in your textbook.