Math Is Fun Forum

4. induction base for 1: n(4*n²-1)/3=1(4*1-1)/3=1
now if we increase n with 1, the sum should increase with (2(n+1)-1)²=(2n+1)²

we replace n in n(4*n²-1)/3 with n+1:

(n+1)(4(n+1)²-1)/3= (n+1)(4n²+8n+4-1)/3=
( n(4n-1) + 8n²+4n+4n²+8n+4-1 )/3=
( n(4n-1) + 12n²+12n+3 )/3=
n(4n-1)/3 + 4n²+4n+1=
n(4n-1)/3 + (2n+1)²

keep posting these ganesh!

i thought about that one too ma+th but i think it wouldnt work since it is two boxes. You cant really take two boxes and put them through eachother

im sorry to bring up an old topic, but i get a lot of different solutions. The problem was on noggintwister and i can make different combinations that all follow the "rules" and all gives different answers....have i missed something, or are the clues wrong? and is that alergic thing, is that some kind of clue?

well actually its true that E=F since in both cases the "values" are the same but E is filled with air, and F is filled with a liquid

an easy and fast approximation of pi that i use is 3+1/7
not that accurate but usually accurate enough

i dont think there need to be any other lifeforms in the universe (it can be so, and i want it, but it doesnt NEED to be like that as some people may think).

lets say there are many, up to billions, paralell universes (or why not an infinite amount of universes?). then lets say that life occurs in one out of 1000000 of these universes, then the chance that there might be life on another place in our universe isnt that big...

Or lets say that this universe will close after a while, since it's now expanding it will implode and when it has shrinked to a dot another big bang occurs and a new universe is created and so it continues. Which means that there have been alot of other universes before this one. Then maybe only 1 out of 1000000 of these universes will have a planet that supports life and then the chance that there may be life on two places in this universe is really low again .

But if this universe is the only one that exists i beleive that there may have been life on other places but if i remember correctly earth existed for a long time before life started to exist and lets say that life will be over on earth in maybe 1000-10000 years, then the period that life exists is very short and the chances they will exist at the same time as us isnt that big (ofcourse life on earth may stay here forever, but at least the chances that there will exist two civilizations at the same time in a universe is imo minimal. but not to forget, the distances in our universe are really huge and then you cant really define what exists at the same time since time is relative, right? )

Ofcourse the chances that a universe will support life may not  be that minimal as i assumed, but the point is that we have really no idea how life really comes up, we really dont know the deepest secrets of life so we can only roughly calculate that chances that a star sould hold a habitable planet, but there may be loads of more conditions that is needed for life that we dont know yet. i only want to prove for all people that are deadly sure we are not alone that this might not be the case.

and as JaneFairfax said, what is life? how do we really define life? is it something that moves, eats, that has a metabolism. The storm systems on jupiter and neptune, that have big storms that appear and disappear, is that life? All life on earth are anyway made by atoms and molecules so you could say that life on earth and the whole evolution may just be a huge mega-advanced chemical reaction.

well since ab is created by the prime factors in c, c must be divisible by ab?

try the same problem but instead of the perimeter, the diagonal is the same on the square and the rectangle!
(this was the problem i first solved since i thought perimeter meant diagonal )

i guessed on:

i dont get it