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
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 :/
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
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.