- #1
James889
- 192
- 1
Hi,
I need some help with mathematical induction
The question is as follows:
prove that [tex]\sum_{i=0}^n (i-3) \geq \frac{n^2}{4}[/tex]
I have shown that it holds for the base step where n=12
[tex]\frac{144}{4} = 36[/tex]
and the sum of all the i's up to 12 [tex]-3,-2,-1,0,+1,+2,+3,+4,+5,+6,+7,+8,+9 = 39[/tex]
[tex]39\geq36[/tex]
Now for the inductive step:
[tex] \sum_{i=0}^{n+1} [/tex]
and i know this can be rewritten, but I am not sure how
either it's [tex]\sum_{i=0}^{n} (i-3)(i-3)~~ \text{or}~~\sum_{i=0}^{n} (i-3)+(i-3)[/tex]
How do i proceed from here?
I need some help with mathematical induction
The question is as follows:
prove that [tex]\sum_{i=0}^n (i-3) \geq \frac{n^2}{4}[/tex]
I have shown that it holds for the base step where n=12
[tex]\frac{144}{4} = 36[/tex]
and the sum of all the i's up to 12 [tex]-3,-2,-1,0,+1,+2,+3,+4,+5,+6,+7,+8,+9 = 39[/tex]
[tex]39\geq36[/tex]
Now for the inductive step:
[tex] \sum_{i=0}^{n+1} [/tex]
and i know this can be rewritten, but I am not sure how
either it's [tex]\sum_{i=0}^{n} (i-3)(i-3)~~ \text{or}~~\sum_{i=0}^{n} (i-3)+(i-3)[/tex]
How do i proceed from here?