Proof by induction

[jspepinc]

infinite chalk boards

[gsagula2]

hauhauah this guy is nuts!

[A08041988]

people these days don't know how to teach math. plain and simple. that god for this guy

[mab4110]

Great lecture. I finally understand it. Wish my professor would give me notes like this.

[ThisIsRiyad]

Cool, but I'm still looking for a deeper proof. I would like to see the summation formulas proven using only algebra, and not by guessing and checking (ie: not by plugging in 1 and equating the right and left side, then finding this to be true -- which we already know by definition of the formulas being, but not yet, proven). Preferably, a proof by deduction would be preferred, since 'deduction is definite' and leaves no assumption other than that the formula is true (which we know anyways).

[vadawaii]

ummm...i quit watching so i dont know if he corrects this, but the summations are wrong in the beginning [at 1:21]...the j cubed should have a 4 in the denominator....

[mrtim111]

@vadawaii its still the same. If you actually square the top and bottom, you would get the denomiator of 4 and the numerator at n²(n+1)²

[bugisami]

@mrtim111 How did you put the superscripts into the comment?

[mrtim111]

@bugisami alt + 0178 is ², alt + 0179 is ³ is all I know.

[Brevan23]

@vadawaii 2 squared = 4

[karla011302]

Execellent....thanks for taking your precious time to do this....omg i was lost, but i just found myself..yay.!!!!

[generalzeedot]

you're entited to at least one bone-headed mistake. that was brill

[lilshortie012]

oh my god. thank you.

you are a life safer, this is so hard trying to learn this when none of my teachers know what to teach...