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if n=1, the sum = 1 - 0 = 1 = n2 assuming true for n ... + (n+1)3 - n3 = n3 + (n+1)3 - n3 = (n+1)3 true for 1, if true for n then true for n+1 so true for all n Σ k3 - (k-1)3 = Σ 3k2 - 3k + 1 = n3 Σk2 = n3/3 + Σk - Σ1/3 = 2n3/6 + 3n(n+1)/6 - 2n/6 = (2n3 + 3n2 + 3n - 2n)/6 = n(2n2 + 3n + 1)/6...

lol that seems to be your answer for everything (well, a couple things at least) the monic + integer coefficients :. rational roots are integers thing is pretty cool. what's the proof for it?

:rolleyes: :rolleyes: :rolleyes: :rolleyes: :rolleyes:

^well that still wouldn't work as there isn't actually a limit

hip hop requires no talent or skill and can be made by a 5 year old, all the songs sing about hos and bitches and slapping them and stuff, it has no artistic qualities or complexity or meaning or any display of understanding of music, doesn't use real instruments, and overall is not interesting...

is that l'hopital's? you can't apply that to the question because the denominator and numerator don't both approach 0 (I know the question was typed out wrongly). and wouldn't the -2 be cancelled out, so your limit would become +7?

was just checking..

everyone knows that you can't express your opinion unless you do english

so (1-0.99...)/(1-0.99...) is undefined (ie. is 0/0)? + it seems to me that the pure/applied distinction seems to only be relevant to university study - to tell you whether the course is related to the applications or not would it probably be best to take mainly pure courses first, and then...

can bad sleep habits have long term/permanent effects on your body, or is it mostly just short/medium term?

well I wouldn't say it takes all that long to do it by parts. I definitely prefer the u=4-x way though

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q I assume you would, unless it said "in its simplest form" or something

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q let x=u, (4-x)1/2 = dv du = dx v = -2/3(4-x)3/2 so I x(4-x)1/2.dx = -2/3 x(4-x)3/2 + I 2/3(4-x)3/2 = -2/3 x(4-x)3/2 - 4/15(4-x)5/2 = (4-x)3/2(-10/15 x - 16/15 + 4x/15) = -2/15 (4-x)3/2(3x + 8) [+C]

Re: 回复: Re: 回复: Re: 回复: Re: Integration Q just do i.b.p

as a school subject I didn't like it at all since it was verrry boring (except in 1st term. most of my subjects were somewhat enjoyable then). I mostly just sat there doing basically nothing

I didn't like any of my subjects :)

I don't remember how the pendulum period formula is derived, but at some point you assume that sin[x]=x, which is only a good approximation for small angles

so you won't have to remember them/look them up I suppose though it's not like there's many that you'd need to remember anyway

I don't think that was the point..

I wonder if he's decided yet?