Mathematical induction

>>8653657
didn't you simplify something incorrectly in the steps between the >= and the next =? it's a multiplication, not an addition

>>8653674
(2n+1)=2(n+1)-1

>>8653657
Use this statement:

∀P((0∈P∧∀i(i∈P-->i+1∈P)) --> ∀n(n∈P))

you forgot to multiply the. (-1/(n+1)) by everything else, 2 rows b4 the ???

Lol just finished doing induction proofs in discrete math. Some of the algebra was pretty annoying and the way to manipulate things was stuff I've never seen

>>8653703
Examples? Did it involve factorials?

I think I have the answer but I don't know latex, so this will take a while to format. Check back in a bit OP.

>>8653657
The crux of the induction hypothesis is that the original proposition is true.

So assume 2n choose n > = stuff.

Then just show 2n+1 choose n+1 > 2n choose n.

If that's true, then 2n+1 choose n+1 >= stuff.

File: test1.gif (3KB, 250x176px) Image search: [Google]

3KB, 250x176px

>>8653913 here, finally done with latex.

Continuing from >>8653657, at the line where you used the induction hypothesis

File: test2.gif (8KB, 370x292px) Image search: [Google]

8KB, 370x292px

>>8654044

>>8653913
I'm gonna go to bed, if you're still about to post something I'll see it in the morning. Thanks for the effort.

>>8653702
Looks like I did, thanks. That didn't help me solve it either though, I think I have a wrong approach altogether.

File: test3.gif (8KB, 523x185px) Image search: [Google]

8KB, 523x185px

>>8654050
And this is it

I used blue to indicate cancelling a term, and gold for annotations

I'm not sure if this is correct though

>>8654052
>>8654050
>>8654044
>>8654053
Oh wow, guess I'm not going to bed then.

>>8654050
Lines 4 - 5 of this image are the same, disregard the duplicate line

Everything else seems correct, but I already spent a few hours looking at this so I'm not the most reliable source. Anyway op, you really ought to use the homework board (>>>/hm/) for these kinds of threads!

>>8654053
Thanks a bunch for this, anon, looks correct to me.
I can rest easy now.